If they all go at each other then I think the Argonians or the Woodelves would win. The argonians because they already own two provinces so they've got s good starting position. And the woodelves because they would sneak around until the other races have butchered each other and then they would kill those who remain.
But in terms of the lore I think the elves are going to retake tamriel, the aldmeri dominion is back and the imperials and nords are fighting among themselves.
it all depends on whoever has the dragonborn on their side.
also, there is a book that details how the khajiit butchered the wood elves. maybe the slave races would team up at first, but cultural differences causes a rupture, and they go to war once again. as much as i love the khajiit, i have to say the argonians have the upper hand in this situation, with their poison and disease immunity. and water breathing. but the khajiit would put up a helluva fight with guerrilla tactics, taking advantage of their nighteye.
but if all races were against eachother, the redguards and orcs would cripple themselves, while the argonians took southern/eastern tamriel. if the redguards and orcs didn't team up, the argonians would take them all. but if they did, the humans and cursed elves would mutilate the argonians.
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