diff --git a/tensordict/_lazy.py b/tensordict/_lazy.py
index 488681dcd..d060beda2 100644
--- a/tensordict/_lazy.py
+++ b/tensordict/_lazy.py
@@ -19,7 +19,7 @@
 import torch
 from functorch import dim as ftdim
 from tensordict._td import _SubTensorDict, _TensorDictKeysView, TensorDict
-from tensordict._tensordict import _unravel_key_to_tuple
+from tensordict._tensordict import _unravel_key_to_tuple, unravel_key
 from tensordict.base import (
     _ACCEPTED_CLASSES,
     _is_tensor_collection,
@@ -133,6 +133,8 @@ class LazyStackedTensorDict(TensorDictBase):
 
     """
 
+    _is_vmapped: bool = False
+
     @classmethod
     def __torch_function__(
         cls,
@@ -362,7 +364,7 @@ def _set_str(
         if not validated:
             value = self._validate_value(value)
             validated = True
-        if self.hook_in is not None:
+        if self._is_vmapped:
             value = self.hook_in(value)
         values = value.unbind(self.stack_dim)
         for tensordict, item in zip(self.tensordicts, values):
@@ -397,7 +399,7 @@ def _set_tuple(
         if not validated:
             value = self._validate_value(value)
             validated = True
-        if self.hook_in is not None:
+        if self._is_vmapped:
             value = self.hook_in(value)
         values = value.unbind(self.stack_dim)
         for tensordict, item in zip(self.tensordicts, values):
@@ -554,7 +556,7 @@ def _set_at_str(self, key, value, index, *, validated):
         if not validated:
             value = self._validate_value(value, check_shape=False)
             validated = True
-        if self.hook_in is not None:
+        if self._is_vmapped:
             value = self.hook_in(value)
         split_index = self._split_index(index)
         converted_idx = split_index["index_dict"]
@@ -649,7 +651,7 @@ def _set_at_tuple(self, key, value, idx, *, validated):
         if not validated:
             value = self._validate_value(value, check_shape=False)
             validated = True
-        if self.hook_in is not None:
+        if self._is_vmapped:
             value = self.hook_in(value)
         item = td._get_str(key, NO_DEFAULT)
         item[idx] = value
@@ -778,10 +780,22 @@ def _get_str(
                     # then it's a LazyStackedTD
                     out.hook_out = self.hook_out
                     out.hook_in = self.hook_in
+                    out._is_vmapped = self._is_vmapped
+                    incr = 0 if not self._is_vmapped else 1
+                    out._batch_size = (
+                        self._batch_size
+                        + out.batch_size[(len(self._batch_size) + incr) :]
+                    )
                 else:
                     # then it's a tensorclass
                     out._tensordict.hook_out = self.hook_out
                     out._tensordict.hook_in = self.hook_in
+                    out._tensordict._is_vmapped = self._is_vmapped
+                    incr = 0 if not self._is_vmapped else 1
+                    out._tensordict._batch_size = (
+                        self._batch_size
+                        + out._tensordict.batch_size[(len(self._batch_size) + incr) :]
+                    )
             elif self.hook_out is not None:
                 out = self.hook_out(out)
             return out
@@ -802,7 +816,7 @@ def _get_str(
     def _get_tuple(self, key, default):
         first = self._get_str(key[0], None)
         if first is None:
-            return self._default_get(first, default)
+            return self._default_get(key[0], default)
         if len(key) == 1:
             return first
         try:
@@ -850,7 +864,7 @@ def _cached_add_batch_dims(cls, td, in_dim, vmap_level):
         # we return a stack with hook_out, and hack the batch_size and names
         # Per se it is still a LazyStack but the stacking dim is "hidden" from
         # the outside
-        out = td.clone(False)
+        out = td.copy()
 
         def hook_out(tensor, in_dim=in_dim, vmap_level=vmap_level):
             return _add_batch_dim(tensor, in_dim, vmap_level)
@@ -869,6 +883,7 @@ def hook_in(
 
         out.hook_out = hook_out
         out.hook_in = hook_in
+        out._is_vmapped = True
         out._batch_size = torch.Size(
             [dim for i, dim in enumerate(out._batch_size) if i != out.stack_dim]
         )
@@ -1570,7 +1585,7 @@ def update(self, input_dict_or_td: T, clone: bool = False, **kwargs: Any) -> T:
             isinstance(input_dict_or_td, LazyStackedTensorDict)
             and input_dict_or_td.stack_dim == self.stack_dim
         ):
-            if not input_dict_or_td.shape[self.stack_dim] == len(self.tensordicts):
+            if len(input_dict_or_td.tensordicts) != len(self.tensordicts):
                 raise ValueError(
                     "cannot update stacked tensordicts with different shapes."
                 )
@@ -1580,36 +1595,37 @@ def update(self, input_dict_or_td: T, clone: bool = False, **kwargs: Any) -> T:
                 td_dest.update(td_source, clone=clone, **kwargs)
             return self
 
-        keys = self.keys(False)
+        inplace = kwargs.get("inplace", False)
         for key, value in input_dict_or_td.items():
             if clone and hasattr(value, "clone"):
                 value = value.clone()
-            else:
+            elif clone:
                 value = tree_map(torch.clone, value)
+            key = unravel_key(key)
             if isinstance(key, tuple):
-                key, subkey = key[0], key[1:]
-            else:
-                subkey = ()
-            # the key must be a string by now. Let's check if it is present
-            if key in keys:
-                target_class = self.entry_class(key)
-                if _is_tensor_collection(target_class):
-                    if isinstance(value, dict):
-                        value_unbind = TensorDict(
-                            value, self.batch_size, _run_checks=False
-                        ).unbind(self.stack_dim)
-                    else:
-                        value_unbind = value.unbind(self.stack_dim)
-                    for t, _value in zip(self.tensordicts, value_unbind):
-                        if len(subkey):
-                            t.update({key: {subkey: _value}}, clone=clone, **kwargs)
-                        else:
-                            t.update({key: _value}, clone=clone, **kwargs)
-                    continue
-            if len(subkey):
-                self.set((key, *subkey), value, **kwargs)
+                # we must check that the target is not a leaf
+                target = self._get_str(key[0], default=None)
+                if is_tensor_collection(target):
+                    target.update({key[1:]: value}, inplace=inplace, clone=clone)
+                elif target is None:
+                    self._set_tuple(key, value, inplace=inplace, validated=False)
+                else:
+                    raise TypeError(
+                        f"Type mismatch: self.get(key[0]) is {type(target)} but expected a tensor collection."
+                    )
             else:
-                self.set(key, value, **kwargs)
+                target = self._get_str(key, default=None)
+                if is_tensor_collection(target) and (
+                    is_tensor_collection(value) or isinstance(value, dict)
+                ):
+                    target.update(value, inplace=inplace, clone=clone)
+                elif target is None or not is_tensor_collection(value):
+                    self._set_str(key, value, inplace=inplace, validated=False)
+                else:
+                    raise TypeError(
+                        f"Type mismatch: self.get(key) is {type(target)} but value is of type {type(value)}."
+                    )
+
         return self
 
     def update_(
diff --git a/tensordict/_td.py b/tensordict/_td.py
index 2e01b91cd..5c34d8fbd 100644
--- a/tensordict/_td.py
+++ b/tensordict/_td.py
@@ -271,11 +271,11 @@ def to_module(self, module, return_swap: bool = True, swap_dest=None, memo=None)
             # For batch-size it is a minor issue (unlikely that a td with batch-size
             # is passed with to_module) but for the device it could be a problem.
             if swap_dest is None:
-                swap = self.empty()
-                swap.clear_device_()
+                swap = TensorDict({}, batch_size=[])
             else:
                 swap = swap_dest
             memo[id(module)] = swap
+            _swap = {}
 
         for key, value in self.items():
             if isinstance(value, (Tensor, ftdim.Tensor)):
@@ -320,8 +320,13 @@ def to_module(self, module, return_swap: bool = True, swap_dest=None, memo=None)
                     swap = swap.to(device=local_out.device)
 
             if return_swap:
-                assert local_out is not None, key
-                swap._set_str(key, local_out, inplace=False, validated=True)
+                _swap[key] = local_out
+        if return_swap:
+            if isinstance(swap, TensorDict):
+                # this is very ad-hoc but faster than calling _set_str every time
+                swap._tensordict.update(_swap)
+            else:
+                swap.update(_swap)
         return swap
 
     def __ne__(self, other: object) -> T | bool:
@@ -1242,12 +1247,13 @@ def _set_str(
         inplace: bool,
         validated: bool,
     ) -> T:
-        best_attempt = inplace is BEST_ATTEMPT_INPLACE
-        inplace = self._convert_inplace(inplace, key)
+        if inplace is not False:
+            best_attempt = inplace is BEST_ATTEMPT_INPLACE
+            inplace = self._convert_inplace(inplace, key)
         if not validated:
             value = self._validate_value(value, check_shape=True)
         if not inplace:
-            if self.is_locked:
+            if self._is_locked:
                 raise RuntimeError(_LOCK_ERROR)
             self._tensordict[key] = value
         else:
@@ -1703,14 +1709,13 @@ def contiguous(self) -> T:
     def empty(self, recurse=False) -> T:
         if not recurse:
             return TensorDict(
-                device=self.device,
-                batch_size=self.batch_size,
+                device=self._device,
+                batch_size=self._batch_size,
                 source={},
-                # names=self.names if self._has_names() else None,
                 names=self._td_dim_names,
                 _run_checks=False,
-                _is_memmap=self._is_memmap,
-                _is_shared=self._is_shared,
+                _is_memmap=False,
+                _is_shared=False,
             )
         return super().empty(recurse=recurse)
 
diff --git a/tensordict/base.py b/tensordict/base.py
index 74e4980f3..e9f0b7b5a 100644
--- a/tensordict/base.py
+++ b/tensordict/base.py
@@ -3125,8 +3125,7 @@ def __exit__(self, exc_type, exc_val, exc_tb):
                 return self.lock_()
             if last_op == self.__class__.to_module.__name__:
                 if is_tensor_collection(out):
-                    with out.unlock_():
-                        return self.to_module(*args, **kwargs, swap_dest=out)
+                    return self.to_module(*args, **kwargs, swap_dest=out)
                 else:
                     raise RuntimeError(
                         "to_module cannot be used as a decorator when return_swap=False."
@@ -3520,6 +3519,10 @@ def flatten_keys(self, separator: str = ".", inplace: bool = False) -> T:
                 result._set_str(
                     leaf_flat, self.get(leaf), validated=True, inplace=False
                 )
+            shared = result._is_shared = self._is_shared
+            mmap = result._is_memmap = self._is_memmap
+            if shared or mmap:
+                result._is_locked = True
             return result
 
     @cache  # noqa: B019