If you really want a thin case, a folio case isn't what you're looking for!
I have the BluRex case, and like it. I prefer the way it attaches the Transformer Prime to the case, using corner clips, covered in material to protect the screen, to the way other cases have a sleeve, which, once the Prime is inserted, covers up a large portion of the screen.
That being said, any folio case will add more then double to the thickness of the TP. A video reviewer of one of these cases (perhaps the BluRex, don't remember) used nickles to measure the Transformer Prime (4 nickels in thickness) compared to the TP with case on (10 nickels).
I'm waiting for one of the cases in this thread
to be released!
Check out this video
, if you want a very thin case!
Considering the Transformer Prime has Gorilla Glass, I'm not that worried about the screen breaking (although, there have been some people who's screen has cracked).
I'm somewhat worried about scratches, as I've read of people who's TP has a scratch or two on the screen, so I'm getting a screen protector (also hate how much fingerprints show up on the Prime).
I figure with a screen protector, and a thin, snap on clear plastic case to protect the back spun metal aluminum back of the Prime, I should be set.
Sorry... don't have tools to accurately measure the BluRex case.