Arnold and Maria -- Battleground: Neiman Marcus

There's only room for one sheriff in Neiman Marcus ... at a time ... at least for Arnold Schwarzenegger and Maria Shriver.

TMZ shoppers spotted Arnold -- with his weird new haircut -- roaming the racks at Neiman's in Bev Hills on Xmas Eve.

Arnold meandered from the overpriced jewelry ... to the extremely overpriced menswear ... to the restaurant area ... and then he left.

Roughly 15 minutes later, guess who appeared? Maria mosied through the department store for some last minute shopping. .

January will be an interesting month for the former couple. Not yet divorced, they are still squabbling over money. So the question -- who will pay the enormous credit card bill?

Stay tuned ...