Oh by the way, you forgot Valenwood. Us poor poor Bosmer...we never get no love. *pout* I'm going to go cry to my tree.
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Ok, but seriously I'll take a stab at this.
Skryim / Cyrodill - I'm doing these both because they pretty much relate to each other. The Empire is going to fall apart, just looking at things now and how much Skyrim is split and even the Empire supporting Nords are looking for a chance to break away it seems. Without Skyrim, I think the Empire dies and Cyrodill becomes it's own province, but it still serves as the metropolitan center of Tamriel because geographically it still is and the Imperials are superb entrepeneurs and businessmen. Certain cultures are excellent seafarers and the like, but Imperials are just fluent in the art of business so they will still be a huge melting pot in terms of continental economy and trade. Skyrim on the other since it broke away will start to build from within and organize and unite the country as it's own. I could eventually seeing them going to war with someone, even if it is for a small piece of territory like Solsteim.
Hammerfell - They are pretty much on their way to doing their own thing. I don't think they would try to counteract the Dominion but it is certainly feasible. Like Skyrim, they're going to focus inward and unite their culture together but at the same time possibly make a new alliance with their neighbors: the Bretons.
High Rock - So with Skyrim and Hammerfell focusing within, I think High Rock undergoes a major shift in their political structure. IIRC, they don't really have a centralized government but instead are more like a nation of city-states. They will see everybody else and need to make decision whether to unite the land under one banner or at least come to a mutual agreement. I think this province will have the most democratic type of society. With that said since the Empire broke apart they will want an ally and I believe the Redguard would be a natural choice. If the Nords and Skyrim want to join, I could see that too.
Orsinium - will stay the same, probably be sacked by someone. Though here is an interesting thought. If the Orcs could somehow gain some strength, maybe...just maybe they make a push for a larger potion of land, taking some from Hammerfell and Skyrim in the mountains. They would truly have a province to call their own...small, but their own. With all the internal rebuilding of Skyrim and Hammerfell, they might actually succeed and they could further their culture (which I would like to see). The Orcs could literally get a new nickname...instead of being the Pariah Folk, they could be Mountain Elves or something.
Summerset Isles / Valenwood - if the Dominion gets pushed back, I could see the Bosmer and Altmer remaining together. They will realize that their (failed) push for forceful dominance left a sour taste in many peoples mouths and will want to have a united front to dissuade anybody from trying to attack them.
Elsweyr - pretty much the same here, but they might break away. However considering their gratefulness to the Dominion I think they will stick by their side. Doing so pretty much solidifies the Dominon's presence in the southern and southwest of Tamriel (plus it's so easy to trick a cat mean come on...you can squirt one with a water pistol from across the room because they're climbing the curtains, and they will run over to you for protection...)
Morrowind - same state they are now, trying to rebuild after the Red Mountain disaster.
Black Marsh - remains independent until they see the need to do an alliance with an outsider, and will continue to look for ways to enact revenge on the Dunmer.