Does the story line for assassins creed 2 continue off of 1 or does brotherhood off of 2

I know for a fact that Ezio (pronounced Etzio) is somehow related to Altair, and you start off escaping from Abstergo industries, so I'd say Assassin's Creed 2 continues off of 1, Brotherhood starts exactly where AC2 finishes with ezio. But with desmond you go to the villa auditore in modern day and you need to do something with him first. Once you have got the animus started you can start playing with ezio.