Kristen Stewart, Robert Pattinson fighting over their dog

After splitting up their living arrangements, Kristen Stewart and Robert Pattinson are reportedly moving on to the next phase of their break-up: the custody battle.

The “Twilight” couple, still reeling from revelations last week that Stewart had an affair with her married director, are in the process of figuring out who will keep their dog Bear, according to RadarOnline.com.

“After Rob moved his things out of their Los Angeles home, he then told Kristen he wanted Bear,” the gossip site cites a source as saying.

Stewart, 22, and Pattinson, 26, adopted the rescue from a Louisiana animal shelter last year while filming “Breaking Dawn.”

"I'm one of those guys who'd adopt a whole animal shelter . . . Thank God that Kristen was with me,” Pattinson reportedly told a German newspaper at the time. “So we just adopted one dog. A mutt. We called him Bear.”

But after photos surfaced last week of Stewart kissing her “Snow White and the Huntsman” director Rupert Sanders, who is married and has two children, Pattinson asked her to move out — and reportedly doesn’t plan to share.

“She was heartbroken — they adopted Bear together and she always felt that he was their little baby,” RadarOnline’s insider said. “However, Kristen won’t give up Bear in a hurry . . . She wants joint custody — and it could get a little messy.”

Gossip Cop disputed the report, citing sources close to the couple who say reports they are fighting over who will keep the pet are "complete b.s."

Stewart has made no secret of her love for Bear, even as she often stayed mum on the status of her relationship with Pattinson, and has been spotted out and about with the dog several times in the last year.

For the couple, who were rumored to be on the road to marriage, adopting the dog proved a chance to play at parenting.

“Bear is literally a child. He’s like my — he’s still a baby,” she told Teen.com in May.

No matter what happens with Bear, Stewart won’t be totally solo in her new life — she seemingly will maintain sole custody of her 8-year-old cat named Max.

“They both love me in very different ways," she told Teen when asked which of her pets loves her more. “Max is like . . . I mean, we live together. He's like my roommate."

And he may soon be the closest thing she has to Pattinson, as well.

"We have a really strong, really weird codependent, almost Bella/Edward relationship," she told People in 2010. "I'm going to be a crazy cat lady one day, I'm sure.”

By Meena Hart Duerson / NEW YORK DAILY NEWS