Largest possible texture size (in game space)? Or: Why does auto tiling happen?

So here is a picture of a very large mesh I have with a material on it. The texture has no tiling and shows as a single square on the preview in the material.

The material itself is on a very large plane. The curving edge is where the plane intersects the skysphere which is 3276800 uu wide. Given how it looks it seems as if there are about 17.5 tiles of the texture visible along the diameter of the skysphere. I infer from this that the largest size a material can be is not related to the mesh which it is on. It seems to be about 187245 uu in width for each tile. Changing the texture group or texture max size doesn’t seem to do anything and I couldn’t find any settings in the material that seemed related.

Changing the scale of the mesh that the material is on WILL increase the texture size (without limit it seems, see attached image).

So assuming a mesh with a world scale of 1 what is the maximum size a material can be in the world?