[1.32] Ahilga, Ahilga, Ahilga

Yes i can confirm you have to kill their soverign too even if you captured all their cities. Afterall, as long as there's still one unit left they still have a chance to retake their city no?

you don't have to kill the sovereign - you can also demand his surrender, which will destroy all remaining cities and outposts and make him your vassal. he basically becomes a champion of your civ and keeps all his ablities and all the stuff he has, though he gets a negative promotion "broken spirit" that reduces his accuracy and spell mastery by 25%. this is usually the best way to end a war of annihilation against an AI, since this also conveniently gives you the faction prestige of the sovereign (basically his level divided by two - just like your own sov). and it gives you access to his sovereign profession (like for example  if you make lord relias a vassal, you get his "adventurer" perk that allows you to recruit champions for free, or if Verga becomes your vassal, unit wages are cut in half sine you inherit his Warlord perk) 

Problem is they wont talk to you about surrender if they got no cities left. And then you have to scout the whole map for that damn sovereign.

I always set Surrender Threshold to Often (which basically means they will consider surrender if you are more than twice (or is it three times?) their faction power and they have few or no cities left).  If they are "too busy to talk" you can still talk to them if there is at least one sovereign you can talk to which you can scroll to the "busy" one.

i guess that trick with the diplo screen could be called an exploit (though it's probably not a gamebreaking one - after all you have to crush them pretty badly for them to surrender; the scroll trick just bypasses the additional hurdle of them refusing to talk to you)

legit alternatives are to leave them a final city and wait until they are willing to talk (the final city gets destroyed, so if possible make sure to conquer the good cities first and leave them a lesser city), or root them in place (freeze/tremor) if they are within your borders until they are willing to talk again.

I usually make them surrender rather then kill them. Even if they don't have good traits you can use them as a governor; and sometimes they have good gear.

Or if your evil there is always steal spirt. A Master Death/Life/Fire mage is fun.

Or even when you're not evil!  I generally play a Cruel Life Adventurer Altarian, and I am cruel with champions I don't like (and who have good magic skills, hehe)...

Has anyone run into the other situation in my OP, that of three cities with the same name founded by the same faction? The other strange part of the game is that two of the factions were founding cities, expanding etc., and the other two founded a single city and a few outposts but no more cities.

i've seen Ai only build one city and a few outposts, but not the pther problem. i guess if a nation loses it's first and only city and the sov is still alive, the sov is allowed to found a new capital- or something along that line