Sources close to the warring couple tell us Rob is cutting Chyna off financially. He'll no longer make payments on her Tarzana rental. He also has the 2 cars he gave her and jewelry as well.

We're told Chyna actually returned the cars and jewelry to Rob. She's fine paying the rent herself -- she's squirreled away money from various appearances as well as their reality show. She's also confident she has earning power post-Rob.

The big ticket item -- supporting Dream. Our sources say Chyna has no intention of going to court for child support, at least for now. We know Rob wants to raise the baby himself, and it doesn't seem Chyna is putting up much of a fight on that front. Fact is ... her other kid, King Cairo, is being raised primarily by Tyga.

It's unlikely in the foreseeable future either one of them will go to court for money or custody. They both have significant issues, and we're told they don't want to risk an adverse ruling by a judge.