I was looking over at this "what should I do with my prophets" question, and realized that I couldn't give good advice because I wasn't sure whether you could prevent another civilization from starting a religion. After all, if you can use your second Great Prophet to convert enough cities that the AI just says "eh, looks like I'm religious already, this'll do," then it makes converting your enemies a much higher priority than enhancing your own religion. And since a given civ's religion is "whatever 50% of my people believe," a civilization might decide that they don't want to change "their own" religion by founding a new one.
So, if you convert an AI opponent's cities before they found a religion, will they give up on founding their own religion? Or will they found a religion anyway and try to spread the good word to their own cities? Does it matter which AI it is?