pixiejmcc
Prince
Precision is needed because you can capture some 1 pop city.
There is only one condition that permits city capture without autorazing: the target city must have reached at one point in the past size 2.
What happens to the city next doesn't matter, even a whipped archer down to size one pop.
Some people believes culture has to do with autorazing, but it doesn't.
Aha that makes more sense. I'd be mighty annoyed if an AI had whipped their wonder spammed, holy city down to one pop and it autorazed
Told you I didn't test it very extensively 
bonus. The unhappiness first only affects cities with the AP religion in them and decays more rapidly the more non AP religions there are in that city. Likely the lone unhappy city has only Hinduism in it.
I didn't test it very extensively but it seems that if the city has 1 pop it autorazes but anything above that and you have the option to take it.