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• Kate Hudson was supposedly holding out hope that she and Alex Rodriguez would reunite one day soon. But it looks like it may be time for Kate to let the dream die. A-Rod's new flame is a "gorgeous blonde" who he met at a gym in Miami. [P6]
• In happier celebrity couple news—and after months of schmoopy public displays of affection—Katy Perry and Russell Brand are now engaged. Brand reportedly proposed while in vacation in India, a trip they decided to take after Perry expressed her love for "Indian culture while they were eating curry." [Us]
• An autopsy has been performed on Casey Johnson, the socialite and pharma heiress who was discovered dead on Monday. There weren't any signs of trauma, but more should be revealed when toxicology tests are completed. In the meantime, friends of Johnson report she went into a diabetic coma on several occasions over the past year, "spent the last months of her life in a suicidal drug haze," and had been living in squalor up until her death, since her family had cut her off. Speaking of the Johnson clan, they're planning to have a private funeral for Casey later this week. [TMZ, NYP, NYDN, People]
• In other Johnson news, she was dealing with a long list of legal problems when she died, including a lawsuit by Porsche (for failing to keep up with her car payments), and another suit by a nanny service (which claimed it was owed money). As for fame addict Tila Tequila, her alleged fiancée, she's been busy posting to Twitter, recounting the "haunting visions" she's been having of Johnson and how they "made such a lovely couple." [TMZ, NYP, Us]

• Lindsay Lohan promised there'd be drama in 2010. And she's now delivering on her word. She says her long-time friend, Patrick "Pootie" Aufdenkamp, stole her sketches for her new 6126 clothing line and has since been banished from LiLo's inner circle, although given how LiLo's fashion career has been going as of late, he probably shouldn't have bothered. [Us]
• Mariah Carey says makeup was responsible for creating the mustache she sports in Precious. But the makeup artist who worked on the movie is denying she did anything to make Mariah look like she had a mustache. So either this is an innocent mix-up or someone is lying. Or maybe this is all an elaborate effort to get you to go out and see Precious? [Us]
• Alexa Ray Joel seems to have really bounced back from her suicide attempt last month: She's now counseling people and doling out love advice on Facebook. ("Through helping others, I feel I am helping myself," she explains). One of Joel's particularly helpful tips for dealing with "heartbreak-related depression"? Taking a hot bath. [NYDN]
• A woman named Shellie Doreen Smith claims she was married to Michael Jackson in the 1970s. She can't remember exactly when, though, but she did remember to file a lawsuit this week and is now asking for a few bucks from Jackson's estate. [TMZ]
• A judge dismissed a battery charge against Gerard Butler for allegedly getting rough with a paparazzo back in 2008. Which is good for Butler, sure, although a few months of exercise in the prison gym yard wouldn't have been the worst thing in the world. [MSNBC]
• Redmond O'Neal, the drug-addled son of Farrah Fawcett and Ryan O'Neal, is in trouble again. He admitted to violating his probation by using drugs during a 24-hour pass from his rehab facility, and he's been sent to a "30-day jail rehab facility." [People]
• Is Lady Gaga's "Monster Ball" Tour losing money—even though it's sold out every night—because she's overspending on extravagant sets? That's what one paper is claiming. [Sun]
• Readers of Esquire's UK edition have named Rachel Weisz the world's "most marriable woman." Interestingly, she's been dating director Darren Aronofsky since 2001, they've been engaged since 2005, and they have a son together, although they still haven't managed to set a date for the big event. Awkward. [Telegraph, DM]
• Did Charlie Sheen and Denise Richards celebrate New Year's Eve together? That's what one website is reporting, although you may want to take the news with a grain of salt (or else wait for Brooke Mueller to go crazytown on someone). [ShowbizSpy]
• Things are supposedly heating up between Miley Cyrus and her boyfriend, Liam Hemsworth. Click through to read all about it, provided you care about Miley Cyrus's love life, of course. [P6]
• If you want to see the steamy sex scene between Zoe Saldana and Sam Worthington from Avatar, you're going to have to wait for the DVD. Director Jimmy Cameron cut it from the big screen version to be sure the movie got a PG-13 rating. [HuffPo]
• The tell-all by Jenny Sanford, who filed for divorce from South Carolina Governor Mark Sanford last month? It's called Staying True and it hits bookshelves on February 5th, in case you care. [NYDN]
• Maybe Ashley Olsen should start up a line of workout clothing? She seems to be a fan of jogging while wearing flannel. [TMZ]
• One sign that Jason Alexander's career could be going better: He's the latest spokesperson for Jenny Craig. He follows such Hollywood greats as Kirstie Alley, Phylicia Rashad, and Valerie Bertinelli. [P6]
• Sharon Stone will appear in four episodes of Law & Order: Special Victims Unit this coming season. She'll play an assistant district attorney. [TVGuide]
• Taylor Lautner's is the highest-paid teenager in America. The 17-year-old will bag $7.5 for his next movie. [ShowbizSpy]
• Videogame company EA Sports said it plans to go ahead with its Tiger Woods online game. No word on whether characters named Rachel, Cori, and Ashley will make cameos. [Us]