At the University of MMA we've been working with Eddie Bravo to establish and promote this. We have it approved at the amateur level in California (with approval from the California State Athletic Commission and CAMO) and down the road we'll try for professional approval.
What is combat jiu jitsu? In a nutshell, it's no-gi BJJ with strikes allowed on the ground (not standing).
It's halfway between BJJ and MMA and it's meant to be a stepping stone for grapplers to transition.
We've done several combat jiu jitsu bouts featuring 10th Planet versus some great schools (eventually we'll do more).
Here's the last bout we promoted! Jorge Pineda (Testai Brazilian Jiu Jitsu / Kings MMA) versus Nate Harris (10th Planet Santa Fe).