Part of what Sweeney’s son has taught her is how important her at-home life is—how, if you let it, work can be all-consuming. “I do have a hard line around my family,” says Sweeney, who avoids morning meetings and tries to leave the office by 6 pm. “For a lot of years, I read every article about time management . . . I think when I finally gave up on the idea of balance, it was a really”—she hesitates, looking for the right word—“happy moment. You can drown in to-do lists. Or you can thrive and have a happy, messy life. Which I do.”

Running such a large empire by definition requires a certain formidability—and Murdoch has described Sweeney as “an iron fist in a velvet glove.” Her off-hours pursuits include hawking, a sport Sweeney characterizes as both beautiful and terrifying. The birds are “magnificent,” she says. “The talons are out, and it’s ready to just grip your wrist.” On the job, though, she prefers to avoid theatrics. “I’m not a screaming, desk-pounding executive,” she says. “I always find it more effective to have a strongly worded conversation.”

Sweeney works hard at bringing humanity to her position, trying to get to know everyone from the marquee talent to the worker bees. With that in mind, she hosts a series called Coffee with Anne, inviting 25 employees she’s never met for a caffeine fix and gabfest. She breaks the ice by sharing something about herself. “I’m sorry I’m late,” she’ll say. “We took our daughter back to college this weekend, and I’m a little upside down.”

Shonda Rhimes, creator of a trio of ABC dramas—the hospital monster hit Grey’s Anatomy; its successful spinoff, Private Practice; and her newest, the political thriller Scandal—describes Sweeney as a calm, reassuring force who “uses her power well, and wisely.” It was Sweeney who introduced Rhimes when the producer was honored with a Visionary Award by Essence magazine last February. “She’s got a great sense of humor and [her intro] was really charming,” Rhimes recalls. “Right before we went up, she turned to me and said, ‘I’m going to do something, and I don’t want you to be mad at me,’ and I was like, Oh my God. What is she going to do?”

Instead of “just getting up and giving a lovely speech about me,” Rhimes says, Sweeney “brought a tiara and crowned me an official Disney princess.”

Given how well Sweeney’s realms performed last year, she deserved a tiara of her own. Even as Disney’s movie division flailed around in the wake of the Martian adventure flick John Carter, deemed one of Hollywood’s costliest flops ever, Disney Media Networks, cochaired by Sweeney and ESPN president John Skipper, was a bright spot at the Mouse House. Six freshman ABC series returned this fall, including breakout hits such as the evening soap Revengeand the fantasy-drama Once upon a Time. In March the Disney Channel toppled ratings juggernaut Nickelodeon from its spot as the most-watched cable network by total daily viewers, and in September, Good Morning America knocked the Today show from its perch. Media Networks revenues grew 9 percent in fiscal 2011, to $18.7 billion. Fiscal 2012 results were not yet available as More went to press, but division revenues for the third quarter were up 3 percent.

Like many of us, Sweeney time-shifts much of her own TV viewing to suit her schedule, and she confesses a special fondness for HBO’s Game of Thrones: “The storytelling is great. I have trouble sometimes with the violence. My husband is a steady viewer, and I’m pretty regular. But he fills in the gaps for me: ‘Oh, you missed it. They killed so-and-so.’ ”