In another question answer bwarner writes:
Once a tile has been claimed, you
can't "steal" it like in Civ 4 (except
using the Great Artist as mentioned in
comments). So you want to make sure
you establish your borders quickly
before another Civ or city-state grabs
those tiles.
Is this accurate? That is, given two enemy cities side by side on the map, one generating a lot more culture, will this still not override the "small" citys borders?
Best Answer
No, there are three possible ways to steal territory:
Culture Bomb with a Great Artist (Vanilla game only)
or
Build a Citadel with a Great General (Gods and Kings ExPack only, see PhysicalEd's answer)
The Traditional Method - just declare war and then capture whichever of their cities "owns" the tile in question.
The Diplomatic Method - convince the Civ in question to give you whichever of their cities "owns" the tile in question as part of a trade or peace agreement. You may find this method easy to achieve if using the Traditional method on some of their other cities first.
With both the Traditional and Diplomatic methods once you are in control of the relevant city you can either keep the city (and so the tile), or you could raze the city so all that land becomes free to be taken (by anyone!) and then purchase the tile/expand culturally from your nearest city.
The serious point here is that once a city unlocks a tile it belongs to that city for the rest of time, regardless of who owns the city, unless the city is destroyed in which case the tiles become "free" for other cities to take ownership.
The culture bomb (or building a citadel in the G&K expansion) is the only exception to this. Doing this captures all of the tiles around the tile where the effect is triggered, and this will take tiles away from any player or city state that had owned them (and I guess it gives them to the nearest city of the bombing player?).
Unlike Civ4, you cannot override a neighbour's borders by racking up a massive culture score in a bordering city.