if im making a map in one game using the quake three engine can i convert it to another game using the same engine or somthing more advanced(i guess)?

Well, you could convert the .map of Quake 3 to a .map of another game running on the same engine. But the transition of certain entities, textures, shaders and other things might make it hairy.

If you are converting then releasing it without the author's permission, that's illegal.

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