She listens, poker-faced, as Redstone tells me, “I would hope she will meet someone nice, who treats her well and isn’t after her money—because she’ll have a lot of money. And I hope she has a baby. She could still have a baby at her age.” In an aside so implausible that it requires suspension of disbelief, Redstone adds, “She is the first lady not just of Viacom, but of Hollywood, and she will continue to be.” At one point, Paula excuses herself to retrieve their four dachshunds, and as she leaves the room, she pinches Redstone’s left earlobe in a showy display of affection.

In a later conversation on the phone, Redstone says, “I’ve told her she can buy any kind of furniture she likes [for the Beverly Hills house]; there’s no limit at all on what she spends. As soon as it’s sufficiently furnished for her to move in, then she’ll move in. In the meanwhile, she stays in this house, and she’s welcome. I want Paula to be happy, to be well-off financially for the rest of her life.” As for dating other women, Redstone claims, “After I’m divorced, maybe. Maybe I will go out with women, but while I’m still married, the only woman I will take out is Paula.”

Their friends talk about their sexual chemistry—and Sumner’s libido. “I had a feeling they were always playfully arguing with each other, saying ‘Go fuck yourself’ and holding hands,” says one frequent dinner companion. “Both of them love to talk about sex. Normally, if you make a dinner appointment with Sumner, he shows up on time, but if they show up 15 minutes, half an hour late, they might say, ‘We had sex four times today!’ ”

But recently, the marriage had become increasingly tempestuous. The Redstones’ profanity-laced arguments were the talk of the entertainment industry. Sylvester Stallone, their next-door neighbor in Beverly Park, figures in a widely repeated anecdote that Redstone denies. According to two Hollywood insiders who spoke with Stallone and his wife, Jennifer Flavin, Redstone erupted a year ago at one of Arnold and Anne Kopelson’s regular Sunday-night movie screenings, when Redstone was anxious to leave and Paula tarried to schmooze with Stallone. “Why don’t you just fuck him already, so we can go home?” Redstone allegedly shouted. Stallone—who friends say was outraged by Redstone’s remark—declines to comment.

Robert Evans, the legendary Hollywood producer who has been friends with the mogul ever since Redstone was an unknown movie exhibitor from Boston trying to strike deals for first-run features, suggests Redstone won’t lack for companionship. “He loves women,” Evans says. “I don’t mean he loves women as a dirty old man. He loves the company of women. And he can be very charming. He plays the piano beautifully, even though his fingers are somewhat distorted from the fire, and he sings.” The 78-year-old Evans, whose seven wives have included Ali MacGraw and Catherine Oxenberg, is no slouch himself. “Next to him, I think I am,” he says. “No kidding.” As to why women are attracted to Redstone, Evans says, “It’s power. Power is a great aphrodisiac. I gave that line to Henry Kissinger.” In the middle of our phone interview, Evans’ secretary interrupts to inform him that Redstone is on the other line and demanding to speak to him right away. “Will you please tell him I’m on the phone?” Evans asks. “I’m afraid,” I overhear the secretary protesting.

Arnold Kopelson probably has the most convincing take on why Redstone’s second marriage didn’t last. “I just think it’s a period where Sumner is now moving on to something else. He spent five very good years with Paula, and I must assume that, for whatever reason, he decided he wanted to move on. Maybe it’s like another business deal.”

Redstone’s apparent inability to separate business from personal dealings is at the heart of the conflict with his family and has major implications for the future of his companies. For years, he hasn’t been on speaking terms with his 58-year-old son, Brent—a former Boston prosecutor who claimed in a 2006 lawsuit (since settled for $240 million) that his father had been denying him his rightful inheritance. Before the falling out, Brent had held a variety of jobs at Viacom and National Amusements, and today he lives on a ranch in Evergreen, Colorado. “I was shocked, and it hurt me,” Redstone says about Brent’s lawsuit. “The lawyers convinced him to do this.” As he talks about his son, he struggles to maintain his composure. “I hope he’s happy doing nothing, living on his farm. I want him to be happy. I told his wife, Annie, that I don’t think it’s right that he’s not doing anything. [Before the lawsuit] I’d offered him various roles in the companies.” Brent, through his lawyer, declined to comment. Sumner’s nephew Michael is also litigating over similar issues. Suing over money seems to be a Redstone family tradition—back in 1972, Michael’s father, Eddie Redstone, sued both Sumner and their father, Mickey, though Sumner says he and Eddie have buried the hatchet.

But the relationship that remains the most volatile, and upon which untold millions of dollars and the fate of an empire rest, is the one between father and daughter. After Sumner’s death, Shari might find herself in a less exalted position than the one she really wants. Her post-Sumner role at Viacom and CBS hinges on a private trust that he established in 2003 to safeguard his 80 percent stake in National Amusements (to Shari’s 20 percent) and set the terms of succession. Shari’s supporters say the trust guarantees her the chairmanship of both public companies; Sumner insists it’s up to the Viacom and CBS boards. Either way, a power struggle seems inevitable.

In the end, she might wind up with the titles but not the power. That’s because she’s just one of four trustees, with just one vote. The other three are Viacom’s Dauman (but pointedly not CBS’s Moonves) and longtime Sumner confidants George Abrams and David Andelman. So one possible scenario is that Dauman, Abrams, and Andelman could band together and decide the outcome of all significant issues, whether Shari agrees or not.

These days, as with virtually everyone else in his life, what Redstone has to say about his daughter is complicated and often contradictory. When he and I meet in L.A., he initially praises her stewardship of National Amusements’ theater chain. “Shari is No. 1 in the exhibition business,” he says. “I consider her to be the best. I’ve never criticized her for her running of the circuits.” But he can’t resist needling: “We don’t always see eye-to-eye. She feels strongly about the exhibition industry, but I don’t think it’s a growth industry.” He also shifts some blame to her for the catastrophic investments that National Amusements made in Midway Games, the videogame company he recently sold for a pittance. “They were all approved by the board, including Shari,” he says. “I’m not passing the buck. But Shari was on the board—I was not. Midway has been very painful.” He says Shari waited too long to change “incompetent” management at the company, of which she was chairwoman before she resigned in November to concentrate on National Amusements’ debt problems.