aetherius (SP?) I think, but theres also a few suggestion's that you end up in the realm of you're patron diety (be it aedra or Daedra)
Example, Big head in Morrowind, end's up in shivering Isles, theres also a few books in the shivering isles which tell you how sheogorath manages to ensnare other princes follower's (often resulting in their deaths) and claim them for his own realm.
but you'll probably get a better answer from a more experience lore buff
People don't go to the shivering Isles because they have died. They all seem to have entered by their own free will. The origin from the idea that people go to some god comes from the Loveletter which mentions that
"Death results in reappropriation of spirit towards its aligned AE?either to the god-planet Aedra or the Principalities of Oblivion." but this means that Daedra return to their principalicity and mortals to the god planets of the Aedra, that is Mundus.
If you as a mortal would go to an Oblivion prince, you'd become immortal because you retain your memory, where as other mortals die, forget and are reborn. Much like Umaril or Mankar Camoran's followers in Paradise actually. Or if you're a god like Vivec or Manimacro, you'd return to your own plane and be reborn from there.