The babolat grips are actually said to be the thickest of the lot.
UPDATE-- I got myself a babolat leather grip, and it's actually thinner looking and feeling than any grip I've used before. Then again, the grip size is smaller too, but it feels a lot smaller than the grip I had on it before (original DNX grip)
Diablo Tour 93, TNT2 16 @ 56#, Prince DuraRib+
And, returning after more than a year under a rock... Amone!