Cheryl Burke is dancing off with a W in the fallout from her divorce with Matthew Lawrence — instead of going to court over custody of their dog … he’s waived the white flag.

New court docs, obtained by TMZ, show the ‘DWTS’ star and her now-ex-husband have struck a deal regarding the battle over who’ll be the primary caretaker of their French bulldog, Ysabella … something they’d been fighting about throughout the proceedings.

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As of now … it looks like Cheryl is going to play dog mom to the pooch, as she was awarded all ownership rights — with ML agreeing to give up all docs/data pertaining to Ysabella, including the title of “pet parent” for their once-shared Home Again service.

There was a trial that was scheduled to take place soon if they didn’t squash this, and it looks like they did that just in the nick of time — with all discovery now being withdrawn.

While Matthew and Cheryl finalized their divorce in September, this was one of the final points of contention … which Cheryl had even addressed publicly, calling Matt’s insistence on fighting her over it “cruel.” As she said in interviews, she always saw it as *her* dog.

Cheryl says she got Ysabella from an ex, and felt entitled to it. In the end, it seems he saw it that way too. Of course, he’s on to new horizons … now in a relationship with Chilli.

While Cheryl and Matt are on the same page over Ysabella, a judge has yet to sign off.

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