diff --git a/swh/dataset/journalprocessor.py b/swh/dataset/journalprocessor.py
--- a/swh/dataset/journalprocessor.py
+++ b/swh/dataset/journalprocessor.py
@@ -57,6 +57,7 @@
         self.assignment = assignment
         self.count = None
         self.topic_name = None
+        kwargs["stop_on_eof"] = True  # Stop when the assignment is empty
         super().__init__(*args, **kwargs)
 
     def subscribe(self):
@@ -73,8 +74,6 @@
             self.handle_committed_offsets()
             if self.assignment:
                 super().process(*args, **kwargs)
-        except EOFError:
-            pass
         finally:
             self.progress_queue.put(None)
 
@@ -92,7 +91,6 @@
         """
         Check whether the client has reached the end of the current
         partition, and trigger a reassignment if that is the case.
-        Raise EOFError if all the partitions have reached the end.
         """
         if offset < 0:  # Uninitialized partition offset
             return
@@ -107,9 +105,6 @@
                 ]
                 self.subscribe()  # Actually, unsubscribes from the partition_id
 
-        if not self.assignment:
-            raise EOFError
-
     def deserialize_message(self, message):
         """
         Override of the message deserialization to hook the handling of the