I'm curious here too, I had a sovereign camping out in my territory in one game, so I attacked him, defeated him and apparently I wiped him off the face of the world (yay!). Then later I attacked another sovereign and he didn't die, he warped back to his capital. Then I was attacked and I lost and while i had cities, I lost the game (but I had lost my initial first city, so maybe it has something to do with not having possession of your capital?)

Can anyone else clarify this, it's hard to work out how this works.

You can only respawn if you:

1) Die in your own or neutral territory

2) Have at least 1 essence point remaining

3) Have a city (any city) under your control to respawn in

So in order to vanquish an enemy sovereign, you generally need to either kill him out away from his lands, or conquer him utterly.

There is one small exception to dying in enemy territory--if a sovereign dies while invading a city, but his troops manage to pull out a win and capture it, he will get to respawn there even though it was technically not his when he died.

That one and the luring trick, leave a city empty to draw him to attack (since he think he'll obviously win), then smack him. Empire gone. I've used both tactics to wipe AIs that are sometimes 3-4 times my power rating. Completely broken. The empire destruction mechanic needs to be looked over.

AI sovereigns really need to not enter enemy territory unless ludicrously well-protected.  I've seen way too many sovereigns go on the offensive all alone without any units at all.

I agree with the idea of inheritance for the AI, but I don't like the idea of my Sovereign dying and having my child rule the empire, simply because the Sovereign is supposed to be YOU, he/she is YOUR avatar in the world, and thus shouldn't be so easily shuffled aside upon death. However, if you were good, you wouldn't let your Sovereign die anyways. Still, the idea of a randomly-generated character taking the throne upon my personal avatar's death doesn't sit too well with me.

This is one of few cases were it actually makes sense to have different ruleset for human players and AI. Keep player on his toes in regard of his sovereign, but have AI sovereigns either more difficult to kill or let dynasty system take its place in case of their death.