05/30/2017
Again, it depends on what you are calling 'state'.
The publisher will have to have some sort of session with the broker and the amount of state associated with that session is broker specific. In most cases, the publisher can open and close the session each time it sends the message if performance is not a concern.
That said, those protocol details are not what people are usually concerned about with state. In client/server the server needs to maintain a list of subscriptions for each client connected. This state creates challenges when building servers that support large numbers of clients. Publishers do not have this overhead since the same message is sent to all subscribers.
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02/24/2014
To continue a little on what Randy posted, the publisher in some cases might have a session to a broker, but the broker will handle the fan-out to all of the subscribers and the publisher may have no knowledge about the list of subscribers. In broker-less system there is no state of any type to a subscriber.
Paul Hunkar - DSInteroperability
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