A Los Angeles judge has ordered Mel Gibson to pay his baby-mama tens of thousands of dollars in back child support and give up his legal fight to charge her rent to live in his home, Breaking Celebrity News has exclusively learned.

Mel, 54, and Oksana Grigorieva, 40, are still locked in a closed courtroom for the latest round in their custody battle over daughter Lucia, one.

But Breaking Celebrity News has learned that inside Los Angeles Superior Court, Judge Scott Gordon told the Oscar-winning actor he could not charge Oksana and Lucia rent to live in his Sherman Oaks, California, home.