diff --git a/docs/composites.rst b/docs/composites.rst
index 7290d473..08b721ee 100644
--- a/docs/composites.rst
+++ b/docs/composites.rst
@@ -202,6 +202,13 @@ Methods
    LazyFixedEmbeddingComposite.sample_ising
    LazyFixedEmbeddingComposite.sample_qubo
 
+
+ParallelEmbeddingComposite
+--------------------------
+
+.. autoclass:: ParallelEmbeddingComposite
+
+
 TilingComposite
 ---------------
 
diff --git a/dwave/system/composites/parallel_embeddings.py b/dwave/system/composites/parallel_embeddings.py
index 5b1e353f..e09596ff 100644
--- a/dwave/system/composites/parallel_embeddings.py
+++ b/dwave/system/composites/parallel_embeddings.py
@@ -109,7 +109,7 @@ class ParallelEmbeddingComposite(dimod.Composite, dimod.Structured, dimod.Sample
         >>> from dwave.system import DWaveSampler
         >>> from dwave.system import ParallelEmbeddingComposite
         >>> from networkx import from_edgelist
-        >>> embedder_kwargs = {'max_num_embs': None}  # Without this, only 1 embedding will be sought
+        >>> embedder_kwargs = {'max_num_emb': None}  # Without this, only 1 embedding will be sought
         >>> source = from_edgelist([('a', 'b')])
         >>> qpu = DWaveSampler()
         >>> sampler = ParallelEmbeddingComposite(qpu, source=source, embedder_kwargs=embedder_kwargs)
diff --git a/dwave/system/composites/tiling.py b/dwave/system/composites/tiling.py
index 05430304..5b547a40 100644
--- a/dwave/system/composites/tiling.py
+++ b/dwave/system/composites/tiling.py
@@ -27,6 +27,8 @@
 for explanations of technical terms in descriptions of Ocean tools.
 """
 
+import warnings
+
 import dimod
 import dwave_networkx as dnx
 
@@ -43,6 +45,13 @@ class TilingComposite(dimod.Composite, dimod.Structured, dimod.Sampler):
     graph of dimensions ``sub_m``, ``sub_n``, ``t``, or minor-embeddable to
     such a graph.
 
+    .. deprecated:: 1.32.0
+        Tiling is generalized in
+        :class:`~dwave.system.composites.ParallelEmbeddingComposite`
+        to handle bigger and non-Chimera source graphs on any structured graph
+        supported by :class:`~dwave.system.samplers.DWaveSampler` (including
+        Zephyr). ``TilingComposite`` will be removed in dwave-system 2.0.
+
     Notation *PN* referes to a Pegasus graph consisting of a 3x(N-1)x(N-1) grid
     of cells, where each unit cell is a bipartite graph with shore of size t,
     supplemented with odd couplers (see ``nice_coordinate`` definition in
@@ -120,6 +129,13 @@ class TilingComposite(dimod.Composite, dimod.Structured, dimod.Sampler):
 
     def __init__(self, sampler, sub_m, sub_n, t=4):
 
+        warnings.warn(
+            "'TilingComposite' has been deprecated since dwave-system 1.32.0, "
+            "and will be removed in 2.0. "
+            "Use 'ParallelEmbeddingComposite' for greater flexibility instead.",
+            DeprecationWarning, stacklevel=2
+        )
+
         self.parameters = sampler.parameters.copy()
         self.properties = properties = {'child_properties': sampler.properties}
 
diff --git a/tests/test_parallel_embedding_composite.py b/tests/test_parallel_embedding_composite.py
index 1af3cb43..05b99587 100644
--- a/tests/test_parallel_embedding_composite.py
+++ b/tests/test_parallel_embedding_composite.py
@@ -144,20 +144,17 @@ def test_composite_propagation(self):
             "T_family": mock_sampler0.properties["topology"]["type"],
             "T_kwargs": {"m": mock_sampler0.properties["topology"]["shape"][0]},
         }
-        try:
-            sampler = ParallelEmbeddingComposite(
-                mock_sampler,
-                source=source,
-                embedder=embedder,
-                embedder_kwargs=embedder_kwargs,
-            )
-            sampleset = sampler.sample_ising({}, J, num_reads=1)
-            self.assertGreater(
-                len(sampleset), 1
-            )  # Equal to the number of parallel embeddings
-        except:
-            print('Test is skipped for now, relies on incomplete pull request:'
-                  'https://github.com/jackraymond/minorminer/tree/parallel_embeddings')
+        sampler = ParallelEmbeddingComposite(
+            mock_sampler,
+            source=source,
+            embedder=embedder,
+            embedder_kwargs=embedder_kwargs,
+        )
+        sampleset = sampler.sample_ising({}, J, num_reads=1)
+        self.assertGreater(
+            len(sampleset), 1
+        )  # Equal to the number of parallel embeddings
+
 
 class TestTiling(unittest.TestCase):
     """Testing for purposes of TilingComposite deprecation. See also testing of