diff --git a/dagster_sqlmesh/controller/base.py b/dagster_sqlmesh/controller/base.py
index b3291a0..890c4aa 100644
--- a/dagster_sqlmesh/controller/base.py
+++ b/dagster_sqlmesh/controller/base.py
@@ -367,7 +367,12 @@ def non_external_models_dag(self) -> t.Iterable[tuple[Model, set[str]]]:
         for model_fqn, deps in dag.graph.items():
             logger.debug(f"model found: {model_fqn}")
             model = self.context.get_model(model_fqn)
-            if not model:
+            if not model or model.kind.is_external:
+                # External models are source tables the project READS, not models it
+                # materialises. They must never become multi-asset outputs (that produces
+                # a phantom asset and collides with any existing asset — e.g. a dlt asset —
+                # that already owns that key). They still surface as dependency edges via
+                # to_asset_outs' dep handling.
                 continue
             yield (model, deps)
 
diff --git a/dagster_sqlmesh/controller/dagster.py b/dagster_sqlmesh/controller/dagster.py
index c0e0343..b6dc4f6 100644
--- a/dagster_sqlmesh/controller/dagster.py
+++ b/dagster_sqlmesh/controller/dagster.py
@@ -45,13 +45,19 @@ def to_asset_outs(
                 asset_tags = translator.get_tags(context, model)
 
                 for dep in model_deps:
-                    if dep.model:
+                    if dep.model and not dep.model.kind.is_external:
                         dep_asset_key_str = translator.get_asset_key(
                             context, dep.model.fqn
                         ).to_user_string()
 
                         internal_asset_deps.add(dep_asset_key_str)
                     else:
+                        # A dependency that is NOT a materialised model of this project —
+                        # either an unmodelled table or an EXTERNAL model. Both are upstream
+                        # asset DEPS, not outputs. (External models resolve to a truthy
+                        # `dep.model`, so they must be routed here explicitly; otherwise they
+                        # would be added to internal_asset_deps without a matching out or dep,
+                        # which Dagster rejects once they are no longer emitted as outs.)
                         table = translator.get_asset_key_str(dep.fqn)
                         key = translator.get_asset_key(
                             context, dep.fqn