It’s not obvious which folder contains custom maps files in Unreal Tournament 3. The folder may not even exist.
Intrepid researcher Patrick Ladwig has the answer:
Look at your Documents folder.
There you will find the folder-structure, ‘My Games\Unreal Tournament 3’.
In there, there should be the folder structure ‘UTGame\Published\CookedPC\CustomMaps’.
If it isn’t, don’t panic – simply create the missing folders.
Put all your files in the CustomMaps folder.
…worked like a charm for me.