What Lisa Kerkorian would like everyone to know about her child-support suit against her Hollywood mogul ex-husband Kirk Kerkorian is that it's a rich-person thing. The kind of disagreement that only a man known as the King of the Las Vegas Strip for his control of such casinos as the Bellagio, MGM Grand and Mirage—and who, she says, carries $10,000 in pocket money and drops $200,000 for a week's vacation—could understand. "Fifty thousand [dollars] a month," she states in court papers of the amount she receives to care for their 3-year-old daughter Kira, "is almost an incalculably small percentage of Kirk's net worth."

Which is one reason she is asking the man Forbes names the 46th richest in the world (with assets worth more than $6 billion) for more: $320,000 a month for costs including private school, food, clothes and entertainment—a very pricey category judging from the $70,000 Lisa, 36, says Kira's first-birthday bash at L.A.'s Hotel Bel-Air cost. While the figure "may seem extravagant," Lisa explains, "it is merely an indication of the lifestyle we led." And the child-support request she filed in L.A. superior court on Jan. 7 is merely what is needed "to maintain Kira in the station of life...befitting the child of Kirk Kerkorian."

That's the problem. According to Kerkorian, 84, the kid's not his—not biologically at least. Citing the "close bond" he had already formed with Kira by the time he claims a DNA test excluded him as her father in late 2000, the thrice-married high school dropout turned tycoon (he also controls MGM Studios) considers himself her "psychological" dad. Lisa's lawyer Stephen Kolodny hedges at his claim, simply saying, "He is the father," and calling it "a particularly cruel tactic to use against a small child." But Kerkorian insists, "I had—and have—no intention of leaving her life or reneging on my promise to provide for her support."

Kerkorian says he played the paternity card—and filed a breach-of-confidentiality suit—after Lisa made "false" claims in her support request and broke agreements not to disclose details of their life. "Finally—and belatedly," he states, "I had had enough." Now he too has demands, most notably the restitution of $3.1 million that Lisa says was "a gift" and he says was not. Not surprisingly, he plans to fight her. Says Kerkorian's divorce lawyer, Dennis Wasser: "To her, Kira is a meal ticket."

He's not talking a Happy Meal either. Lisa Bonder grew up in Saline, Mich., the ambitious daughter of upper-middle-class parents (her father was part owner of a local tennis club). A child tennis whiz, she went pro at 16 and was in the U.S. Top 10 before she fell in the rankings and quit in the late '80s. In 1988 she married wealthy L.A. businessman Thomas Kreiss and had their son Taylor, now 12. In 1991 she began a romance with Kerkorian, whom she had met years earlier through a friend, and was soon divorced from Kreiss. As Kerkorian's companion, she says, they traveled the world on one of his private planes or his yacht, regularly spending $6,000 a night for a hotel room. "She liked nice things," tennis coach Nick Bollettieri says of his ex-student. "She enjoyed the spotlight."

What happened out of that spotlight is now a matter of dispute. Lisa says they lived together on and off for nine years on his $13 million, 23-acre property just outside Beverly Hills. He says that while they dated sporadically, they stopped cohabiting in 1995. Either way, they agree that in June 1997 they had what Kirk calls "a weeklong reconciliation," and three months later Lisa told him she was pregnant. According to Kerkorian, who has two adult daughters from his previous marriages, she said she was "absolutely certain" he was the father, and he took her "at her word." Devoted to Kira, he filled his homes with "every imaginable toy," says Lisa. He also bought the Beverly Hills home where Lisa, Kira and Taylor still live. But by her own account, Lisa wanted more. In 1999, worrying that she was "depressed" about being the "mother to our out-of-wedlock child," Kerkorian agreed to her request that he marry her. The point of the ceremony, both say, was "to legitimize" Kira; Lisa promised in advance to divorce him after one month and to waive all spousal-support rights and property claims since, she now says, she hoped "he would let the marriage stand."

She hoped wrong—and the current battle is not limited to the courtroom. On Christmas Eve, court papers allege, Kira received a Mickey Mouse phone and a live bunny rabbit from her dad. But the next day, angered by Kirk's refusal to talk to her, Lisa went to his mansion, smashed the phone in his courtyard—and threatened to "throw the rabbit" next. "It's all very sad," says Lisa's longtime tennis associate, former pro Carling Bassett-Seguso. Mostly for Kira. Her parents, after all, have always known the rules. As coach Bollettieri puts it: "When you play, you pay."

Karen S. Schneider
Lyndon Stambler and Champ Clark in Los Angeles

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Caring for Kira
A partial list of Lisa Kerkorian's monthly child support demands

Nannies $6,850 Security guards $47,450 Vacation home in France $29,296 Eating out $5,920 Household staff $13,216.67 Lessons and tutors $3,386 Food and care for pets $436 Clothing and shoes $2,500 Attorneys' fees $16,704.99