City State Belief buildings

There are several buildings which a player can have if he first selects a specific Belief, and then buys them with Faith points. Those are Cathedrals, Monasteries, Mosques, and Pagodas. The player can add one of those to his cities, using Faith from all his cities, but very possibly those Faith points may have been generated by the city that constructs the building. The basic point is that a city can be generating Faith points, and Faith points _may_ be used to build the appropriate building.

In the case of City States -- heck, even other cities in other civs -- I'm wondering if they EVER use their Faith points to build an associated Belief building? I've seen them create Great Prophets, but there's no way to see what buildings a CS builds. (Particularly if Espionage is turned off.) As Venice I can buy a CS and then see what structures exist. But in that case the absence of any Belief buildings wouldn't prove that CSs don't build them; it just may mean _that one_ never got around to building one before the CS was purchased.

I ask because it would be useful to know if converting a CS can become self-perpetuating Religious expansion. Does the CS create _any_ pressure on its own, or is it up to the player to do ALL of the heavy lifting? In which case it would be useful for a player to be able to use some of his Faith points to place a Belief building in any CS or foreign city that has his Religion as the locally dominant Religion.

they don't create great prophets, they re-capture them from Barbarians, right?

Dunno about CS purchasing faith buildings but I would suspect the GP came from a faith orientated CS. On a side note I've seen a CS generate a GG so I assume they sort of play the game the usual AI's do, like generating culture(some more than others).

To answer your question about spreading, you need to do the heavy lifting, any religious AI's nearby will probably convert those CS's to their religion. Any city that has a majority religion will exert pressure on every city within a 10 hex radius(13 with itinerant preachers). Use this fact to plan which CS to convert first, and possibly your city settle locations.

The CS does not produce Wonders, Settlers, Missionaries or Great People, so the Great Prophet was most likely as a result of a war. THe Great Prophets, like missionaries, are not killed, but simply captured like workers.