Both parties are well and truly smitten with the mutt they adopted together from a Shelter in New Orleans.
According to Radar Online, Rob told K-Stew he wanted to keep Bear after moving out of the couple's $6 million LA pad over the weekend.
But she's not willing to give up without a fight.
"She was heartbroken — they adopted Bear together and she always felt that he was their little baby," a source told the website.
Kristen is particularly close to the pooch since helping him fight Parvo disease as a puppy, said the source.
But a "devastated" Rob reckons he needs Bear for comfort since finding out Kristen cheated on him with her Snow White director Rupert Sanders.
"Rob was so hurt by Kristen's actions he decided that he wants the dog to help him get over what happened. After all, a dog is a man's best friend and Bear is such a good companion," said the source.
We're leaning towards Team R-Pattz on this one, given the 26-year-old has reportedly turned into a lonely, video game-playing geek.
A friend of the actor told The Sun, "Robert has resorted to asking strangers out to keep him company.
"He went out for drinks with a woman staying in his hotel and he told her it was 'ridiculous' he had nobody to talk to. He's been spending most of his day off playing computer games."
It's lucky these two didn't have any kids!
