10/4/2004: It shuffles itself into the owner's library no matter where it would go to the graveyard from.
10/4/2004: Its power and toughness are continuously calculated.
10/1/2008: The ability that has you shuffle Serra Avatar into your library is now a triggered ability. This means that other abilities which would trigger on the Avatar being put into a graveyard will also trigger.
10/1/2008: Whether or not the ability triggers depends on if the Avatar has the ability while in the graveyard. If it doesn't (thanks to Yixlid Jailer, for instance), then the ability won't trigger. It doesn't matter whether the Avatar had the ability in its previous zone (it will trigger even if it had been on the battlefield with Humility).