My guess is that he dies in the battle which is still going on even as we speak.I don't think Ankin kills him.It would be pointess for that to happen.
According to a new hope Darth Vador helps the empire hunt down all the jedis and kills them.So maybe he is force to join the darkside and says no and the empire has him killed.
Nether way we will be finding out soon!JM
Okay, I know I'm most likely wrong but I wanna put my theory in here anyway. First, I wanna say that I think it will be Anakin, not Mace, that kills Dooku. It'll be the same deal as in RotJ when Luke fought Vader in front of Palpatine, but this time it'll be Anakin fighting Dooku in front of Palpatine. But this time, unlike Luke, Anakin will deal the killing blow, completing his path to the dark side. Everything will be parallel to RotJ except Anakin will kill his opponent.
Mace will go alone to confront Palpatine because he knows something's up. Palpatine will reveal himself as the Sith Lord Sidious and Mace and Sidious will duel. Anakin won't be around (why, I'm not sure, I just think he won't be there), so Sidious will be the one to finish off Windu. Anakin will be off doing some assignment for Sidious or something, I dunno.
I just thought I'd say that. ^_^