Kate Moss and Jamie Hince in dog fight

Kate Moss and Jamie Hince are set for a custody battle over their pet dog.

The 41-year-old supermodel is rumored to have split from The Kills rocker, and though he wants to take Staffordshire Bull Terrier cross Archie – who he rescued from Italy – with him to Los Angeles, the British beauty and her daughter Lila, 12, are devoted to the pooch and want to keep him with them.

A source said:  »So far things have been amicable, but the subject of Archie is really tricky and neither knows how to resolve the problem. »

Though Archie belongs to Jamie, Kate has always showered him with attention and gifts.

The source added to the Daily Star newspaper:  »Kate also loves Archie and even took him to a dog whisperer when he was having anxiety problems.

 »She spends a fortune on his accessories and often walks him. »

The 46-year-old rocker has previously admitted to making long-distance phone calls to stay in touch with Archie when he is away on tour.

He is said:  »I get regular updates from Kate on how he’s doing.

 »He’s pretty perfectly behaved. I speak to him on the phone sometimes.

 »He came from the deepest, wildest countryside in Italy. He was almost feral. He needed me, so I adopted him. »