Magento - phpBB3 - Kunena - RokBridge Specialist
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Use the Thank You and Life Preserver Buttons!
Your signature is also great place for setup details...help us help you!
This is run, as the others have mentioned, on Simple Machines Forum. It is not a component, but a stand-alone application that is integrated with Joomla via a bridge.
I'll have to agree--SMF is the best forum. I started using phpbb, but I have found SMF to be a much better product--particularly from an admin standpoint.