diff --git a/test/test_rb.py b/test/test_rb.py
index 5a849224117..35fc37b400c 100644
--- a/test/test_rb.py
+++ b/test/test_rb.py
@@ -2514,14 +2514,15 @@ def _make_data(self, datatype, datadim):
 
     @pytest.mark.parametrize("datatype,rbtype", datatype_rb_pairs)
     @pytest.mark.parametrize("datadim", [1, 2])
-    def test_rb_multidim(self, datatype, datadim, rbtype):
+    @pytest.mark.parametrize("storage_cls", [LazyMemmapStorage, LazyTensorStorage])
+    def test_rb_multidim(self, datatype, datadim, rbtype, storage_cls):
         data = self._make_data(datatype, datadim)
         if rbtype not in (PrioritizedReplayBuffer, TensorDictPrioritizedReplayBuffer):
             rbtype = functools.partial(rbtype, sampler=RandomSampler())
         else:
             rbtype = functools.partial(rbtype, alpha=0.9, beta=1.1)
 
-        rb = rbtype(storage=LazyMemmapStorage(100, ndim=datadim), batch_size=4)
+        rb = rbtype(storage=storage_cls(100, ndim=datadim), batch_size=4)
         rb.extend(data)
         assert len(rb) == 12
         s = rb.sample()
diff --git a/torchrl/data/replay_buffers/replay_buffers.py b/torchrl/data/replay_buffers/replay_buffers.py
index d507e02b24b..af43771ac82 100644
--- a/torchrl/data/replay_buffers/replay_buffers.py
+++ b/torchrl/data/replay_buffers/replay_buffers.py
@@ -253,35 +253,30 @@ def __init__(
         self._batch_size = batch_size
         if dim_extend is not None and dim_extend < 0:
             raise ValueError("dim_extend must be a positive value.")
-        self._dim_extend = dim_extend
-        if self.dim_extend > 0:
-            from torchrl.envs.transforms.transforms import _TransposeTransform
-
-            if self._storage.ndim <= self.dim_extend:
-                raise ValueError(
-                    "The storage `ndim` attribute must be greater "
-                    "than the `dim_extend` attribute of the buffer."
-                )
-            self.append_transform(_TransposeTransform(self.dim_extend))
+        self.dim_extend = dim_extend
 
     @property
     def dim_extend(self):
-        dim_extend = self._dim_extend
-        if dim_extend is None:
-            if self._storage is not None:
-                ndim = self._storage.ndim
-                dim_extend = ndim - 1
-            else:
-                dim_extend = 1
-            self.dim_extend = dim_extend
-        return dim_extend
+        return self._dim_extend
 
     @dim_extend.setter
     def dim_extend(self, value):
-        if self._dim_extend is not None and self._dim_extend != value:
+        if (
+            hasattr(self, "_dim_extend")
+            and self._dim_extend is not None
+            and self._dim_extend != value
+        ):
             raise RuntimeError(
                 "dim_extend cannot be reset. Please create a new replay buffer."
             )
+
+        if value is None:
+            if self._storage is not None:
+                ndim = self._storage.ndim
+                value = ndim - 1
+            else:
+                value = 1
+
         self._dim_extend = value
         if value is not None and value > 0:
             from torchrl.envs.transforms.transforms import _TransposeTransform
diff --git a/torchrl/data/replay_buffers/samplers.py b/torchrl/data/replay_buffers/samplers.py
index c40921e3c99..690a96e5bf7 100644
--- a/torchrl/data/replay_buffers/samplers.py
+++ b/torchrl/data/replay_buffers/samplers.py
@@ -910,7 +910,8 @@ def _sample_slices(
         if (lengths < seq_length).any():
             if self.strict_length:
                 raise RuntimeError(
-                    "Some stored trajectories have a length shorter than the slice that was asked for. "
+                    "Some stored trajectories have a length shorter than the slice that was asked for ("
+                    f"min length={lengths.min()}). "
                     "Create the sampler with `strict_length=False` to allow shorter trajectories to appear "
                     "in you batch."
                 )
diff --git a/torchrl/data/replay_buffers/storages.py b/torchrl/data/replay_buffers/storages.py
index b1dda223f17..186810315c3 100644
--- a/torchrl/data/replay_buffers/storages.py
+++ b/torchrl/data/replay_buffers/storages.py
@@ -147,6 +147,14 @@ def shape(self):
             f"Please report this exception as well as the use case (incl. buffer construction) on github."
         )
 
+    def _max_size_along_dim0(self, *, single_data, batched_data):
+        if self.ndim == 1:
+            return self.max_size
+        raise RuntimeError(
+            f"storage._max_size_along_dim0 is not supported for storages of type {type(self)} when ndim > 1."
+            f"Please report this exception as well as the use case (incl. buffer construction) on github."
+        )
+
     def flatten(self):
         if self.ndim == 1:
             return self
@@ -475,7 +483,7 @@ def _len(self, value):
     def _total_shape(self):
         # Total shape, irrespective of how full the storage is
         _total_shape = self.__dict__.get("_total_shape_value", None)
-        if _total_shape is None:
+        if _total_shape is None and self.initialized:
             if is_tensor_collection(self._storage):
                 _total_shape = self._storage.shape[: self.ndim]
             else:
@@ -497,12 +505,29 @@ def _len_along_dim0(self):
             len_along_dim = len_along_dim // self._total_shape[1:].numel()
         return len_along_dim
 
-    @property
-    def _max_size_along_dim0(self):
+    def _max_size_along_dim0(self, *, single_data=None, batched_data=None):
         # returns the max_size of the buffer along dim0
         max_size = self.max_size
         if self.ndim:
-            max_size = max_size // self._total_shape[1:].numel()
+            shape = self.shape
+            if shape is None:
+                if single_data is not None:
+                    data = single_data
+                elif batched_data is not None:
+                    data = batched_data
+                else:
+                    raise ValueError("single_data or batched_data must be passed.")
+                if is_tensor_collection(data):
+                    datashape = data.shape[: self.ndim]
+                else:
+                    for leaf in torch.utils._pytree.tree_leaves(data):
+                        datashape = leaf.shape[: self.ndim]
+                        break
+                if batched_data is not None:
+                    datashape = datashape[1:]
+                max_size = max_size // datashape.numel()
+            else:
+                max_size = max_size // self._total_shape[1:].numel()
         return max_size
 
     @property
@@ -511,7 +536,8 @@ def shape(self):
         if self._is_full:
             return self._total_shape
         _total_shape = self._total_shape
-        return torch.Size([self._len_along_dim0] + list(_total_shape[1:]))
+        if _total_shape is not None:
+            return torch.Size([self._len_along_dim0] + list(_total_shape[1:]))
 
     def _rand_given_ndim(self, batch_size):
         if self.ndim == 1:
@@ -815,7 +841,10 @@ def _init(
 
         def max_size_along_dim0(data_shape):
             if self.ndim > 1:
-                return (-(self.max_size // data_shape[: self.ndim - 1]), *data_shape)
+                return (
+                    -(self.max_size // -data_shape[: self.ndim - 1].numel()),
+                    *data_shape,
+                )
             return (self.max_size, *data_shape)
 
         if is_tensor_collection(data):
diff --git a/torchrl/data/replay_buffers/writers.py b/torchrl/data/replay_buffers/writers.py
index 9c7ba6f4fb7..bdaa5d573fb 100644
--- a/torchrl/data/replay_buffers/writers.py
+++ b/torchrl/data/replay_buffers/writers.py
@@ -134,7 +134,9 @@ def add(self, data: Any) -> int | torch.Tensor:
         index = self._cursor
         _cursor = self._cursor
         # we need to update the cursor first to avoid race conditions between workers
-        self._cursor = (self._cursor + 1) % self._storage.max_size
+        self._cursor = (self._cursor + 1) % self._storage._max_size_along_dim0(
+            single_data=data
+        )
         self._storage[_cursor] = data
         return self._replicate_index(index)
 
@@ -149,14 +151,15 @@ def extend(self, data: Sequence) -> torch.Tensor:
         if batch_size == 0:
             raise RuntimeError("Expected at least one element in extend.")
         device = data.device if hasattr(data, "device") else None
+        max_size_along0 = self._storage._max_size_along_dim0(batched_data=data)
         index = (
             torch.arange(
                 cur_size, batch_size + cur_size, dtype=torch.long, device=device
             )
-            % self._storage.max_size
+            % max_size_along0
         )
         # we need to update the cursor first to avoid race conditions between workers
-        self._cursor = (batch_size + cur_size) % self._storage.max_size
+        self._cursor = (batch_size + cur_size) % max_size_along0
         self._storage[index] = data
         return self._replicate_index(index)
 
@@ -205,7 +208,7 @@ class TensorDictRoundRobinWriter(RoundRobinWriter):
     def add(self, data: Any) -> int | torch.Tensor:
         index = self._cursor
         # we need to update the cursor first to avoid race conditions between workers
-        self._cursor = (index + 1) % self._storage.max_size
+        self._cursor = (index + 1) % self._storage.shape[0]
         if not is_tensorclass(data):
             data.set(
                 "index",
@@ -224,10 +227,10 @@ def extend(self, data: Sequence) -> torch.Tensor:
             torch.arange(
                 cur_size, batch_size + cur_size, dtype=torch.long, device=device
             )
-            % self._storage.max_size
+            % self._storage.shape[0]
         )
         # we need to update the cursor first to avoid race conditions between workers
-        self._cursor = (batch_size + cur_size) % self._storage.max_size
+        self._cursor = (batch_size + cur_size) % self._storage.shape[0]
         # storage must convert the data to the appropriate format if needed
         if not is_tensorclass(data):
             data.set(