That depends. Were they devout Daedra worshippers? If so, then they would presumably go to that Princes plane.
If the person was almost anyone else, then their soul would be recycled through the Dreamsleeve (basically reincarnation) or perhaps go to Aetherius
Presumably their soul is claimed by Molag Bal, their creator. Cyrodillic Vampires seem to have a pact with Clavicus Vile, so to each their own I suppose
Well, I think that if they're devout/zealous enough then they would be claimed by that Prince. If you're just a "casual" worshipper then its the dreamsleeve for you
More than one Prince? Not sure, but chances are you favor one more, or one of them pays more attention to you. The one that actual gives a [censored] about you would probably get you. And again, passive/casual worshippers are recycled through the dreamsleeve
They seem to beleive in reincarnation
Atheists dont exist, you can choose not to worship a god but you cant deny their existence. For these non-religious people, they would likly go through the dreamsleeve and be reincarnated.
the Imperial pantheon seems to beleive in going to Aetherius as a sort of "heaven" where they go after death
They worshipped the same way as the present people do on Nirn. Nede's likely believe in Sovngarde
Aldmeri belief seem to believe in reincarnation and some sort of enlightenment through Auriel.
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