Found the answer it is.
END CONVERSATION '8EBFD527-E1C2-DC11-94CB-00123FFF2501' WITH CLEANUP ;

Thanks Anyway,
jc

I see you've found the solution, but I think you still might have some work
to do.  It sounds like your conversations are getting ended by one side, and
not by the other side.  Ending a conversation, just like any other SSB
activity, is a two-way thing.  Much like saying goodbye on the phone; it's
rude to simply hang up :-) ... your SSB programs should watch for
EndConversation messages, and end the conversation on that end if one is
received from the other end.

Hi John,

I, too, am getting an accumulation of rows in sys.conversation_endpoints on
the target side of my communications.

Adam is right, that you need to handle the end dialog messages.

Here's an excerpt from a service process on the target side:
SEND ON CONVERSATION @lclConversationID
 MESSAGE TYPE [http://schemas.musicbeat.com/sam/RegResponseMsg (
  @lclResponseMessage
 );
-- End the conversation
END CONVERSATION @lclConversationID;

Here's an excerpt from a service process on the initiator queue

IF (@lclMsgName = 'http://schemas.microsoft.com/SQL/ServiceBroker/EndDialog')
BEGIN
 END CONVERSATION @lclConversationID;
END

I'm using this pattern, but continue to get an accumulation of rows in
sys.conversation_endpoints. I have been digging for a bit on this, and
suspect (though I'm not certain) that I might be seeing bug #50001503:

http://support.microsoft.com/kb/940287

The description of this bug seems to match my symptoms. Does it seem to
match yours?

I have begun to run through the list of possible workarounds described in
the bug, as I'm reluctant to apply the hotfix until I'm positive that I'm
really seeing this bug.

The hotfix is not in the Cumulative update package 5 for SQL Server 2005
Service Pack 2.

http://support.microsoft.com/kb/943656/en-us

I would appreciate learning if you're seeing the same thing in your
application. And if you are seeing any effect from the workarounds or the
hotfix (if you're more courageous than me about applying such things).

Thanks,
--Craig.