Who owns each province of Tamriel ?
Yes, Skyrim belong to the Nords, Hammerfell belong to the Redguard, Black Marsh to Argonians and all of that. But It's not really this way that it works, since Nords, for example, needed to declare war in their own land to seek what they desire.
Which province of Tamriel belongs to the Empire and which belongs to other factions ? All of them.
In the Fourth Era of course.