If I raze a conquered city its territory returns to neutral ownership. However suppose I have multiple cities clustered together, it is not always possible to know which tiles I will lose when razing a city.
Since I am a relatively peaceful player I have not had the chance to experiment with this game mechanic.
So what are the rules which dictate which tiles belong to a particular city when it is razed?
So based on Fabian's answer here combined with Oak's experience mentioned in the comments for this question, it sounds like razing a city will cause all tiles that were acquired by that city to become neutral, as well as all tiles in the immediate ring around that city, even if those tiles were not initially acquired by the city being razed (beacuse as Fabian pointed out, building/capturing a city will automatically transfer ownership of tiles in that inner ring that belong to other cities of the same player to the "new" city). Any tiles in the inner ring that do not belong to the player owning the city should not become neutral.
Unfortunately, I am not aware of any way to determine ahead of time which city initially acquired a tile and thus "owns" it for purposes such as this.