I was wondering if there was any evidence of who was Archmage in Vvardenfell before Trebonius was put in place? Also, what happened to him/her? Also, how does the Archmage system work? Does each district have its own Archmage, and do they all answer directly to Ocato/whoever the Guild Head would be at the time? (And the Imperial Battlemage is also the head of the Mages' Guild, right? [Sorry, haven't played Oblivion enough to know]) If no one knows who the Archmage was before Trebonius, then I smell a quest mod in the making...

http://www.imperial-library.info/cyrodiil_guilds/mages_guild.shtml

That article was definitely helpful about the Mages' Guild leadership and presence in Cyrodiil, but it didn't answer my questions of Archmages in Morrowind/Vvardenfell. Thank you, though!

as far as I know, there are almost never any registers of guildmasters before the current, when the player shows up, the only that is, as far as I know, is in the Thieves Guild of Cyrodiil....

Apparently the island of Vvardenfell only officially re-opened for settlement a few short decades before the events of Morrowind, so if Trebonious wasn't the first then there couldn't have been more than one or two before him. As for what their names might have been if they existed at all - unknown.

Not sure about his predecessors but as far as I know there are 2 archmages in morrowind, Vivec's and almalexia's. Trebonius mentions it in his dialogue when you get some dwemer books translated.
And I'm pretty sure that the battlemages are a separate organisation from the Mages guild.

Separate but connected in some way, since there are a lot of Battlemages guarding the Arcane University.