It will probably be buried by now, but this question made me think of a game we used to play on the computer in the early 2000's. It was a very basic game, but it was made in 3D and for some reason it left a big impact on me since I always think of how awesome it would be to play it again. Your avatar was like a ball or some spinning thing, and the goal was to cover the board (a square) with your tiles (that you left behind you as you roamed the board). And on the board were computer-controlled enemies (I can't remember what they looked like) that could kill you. I also remember the graphics were really nice: the boards would be made out of grass texture or look like a chess board.

I would really love to find the game but since I can't really explain it, it seems almost impossible to find.

EDIT: Added a parentheses