Now that Kate Moss has checked into an Arizona rehab clinic to atone for her coke-induced PR debacle, she’ll have plenty of time to deal with the most tragic aspect of her ordeal—reports that her ex-boyfriend, Jefferson Hack, is seeking sole custody of their two-year-old daughter, Lila Grace. Unlike her other issues, however, we hear this one could be resolved with a simple DNA test.

According to sources close to the model, rumors have been circulating London fashion circles for years that Lila’s true father is not Hack—globetrotting editor of Brit mags Dazed & Confused and Another—but chronic bed-hopper Jude Law.

Sadie [Frost, Jude’s ex] and Kate are best, best friends, and Jude and Sadie were huge into couples swapping and orgies,” says a friend of the former couple. “They had group sex where absolutely everything was okay.”

Meanwhile, fallout from Moss’s ouster by prominent Euro fashion houses H&M and Burberry has triggered panic among stateside fashionistas about an impending crackdown on the slimming drug.

“Kate has always had a horrible cocaine problem, but for these companies to dismiss her now is ridiculous because people will only start hunting for the other ones,” says one top fashion editor. “All the girls are doing coke again. If you held everyone to the same standard, no one would be left to model the freakin’ clothes!” Neither Moss’s lawyer, publicist, nor agent returned phone calls or e-mails seeking comment by press time.