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The story in “Frozen,” the blockbuster Disney musical, did not originally center on two sister princesses. Based loosely on “The Snow Queen” fairy tale, it always had a pair of girls at its core, but it wasn’t until several years into the production process, at a story meeting in the company’s Burbank, Calif., headquarters, that someone suggested that Elsa and Anna be siblings.

Suddenly, “everything started to click,” said Chris Buck, a director of the film. They convened what they called a “sister summit,” for Disney staff to kvetch and gush about their family members. “We got a lot from that,” Buck said.

Still, the older Elsa (voiced by Idina Menzel) and the plucky Anna (Kristen Bell) were not the simpatico kind of sisters. “At the time, Anna was this perfect, perfect princess,” said Kristen Anderson-Lopez, a composer for the film with her husband, Robert Lopez. “And Elsa was really just jealous.”

It was only when the Lopezes delivered Elsa’s anthem, “Let It Go,” an Oscar front-runner for best song, that the characters, and the movie’s true story line, revealed itself.

“The minute we heard the song the first time, I knew that I had to rewrite the whole movie,” said Jennifer Lee, the screenwriter and co-director.

“Frozen,” which is on its way to earning $1 billion globally, is the rare kind of hit, even for Disney, that goes beyond the multiplex, with a chart-topping soundtrack and a stage musical in the works. And “Let It Go” has been the engine of that runaway success. It’s also the centerpiece of perhaps the coolest Oscar category this year, best song: All the nominees are superstars, whether from indie rock, pop, R&B or Broadway. Karen O, frontwoman of the Yeah Yeah Yeahs, is nominated for “Moon Song,” written with Spike Jonze, for his film “Her.” Pharrell Williams, whose 24-hour-video for “Happy” is its own cultural sensation, is a contender for that song, from “Despicable Me 2.” And U2 garnered the only nod for the biopic “Mandela: Long Walk to Freedom,” with its historically rooted “Ordinary Love.”

They are all due to perform at the Oscars on March 2, competing against Menzel’s rendition of “Let It Go,” an emotional juggernaut in which her character transforms from an isolated, troubled queen to a powerhouse of self-acceptance. It has already spawned a legion of YouTube covers (some viewed millions of times themselves) and been certified platinum.

The song had humble roots, though. Anderson-Lopez and Lopez, a Tony winner for the musicals “Avenue Q” and “The Book of Mormon,” started banging it out on the piano at their home studio in Brooklyn. Anderson-Lopez suggested the multipurpose hook “let it go” to Disney: “It was about letting your past go, and also letting your power go,” she said. As background, the couple listened to Adele and musicians like Aimee Mann, “the more tortured singer-songwriters, who talk about keeping secrets and having things that they’re fearful and they’re ashamed of,” she said. One day, they took a walk to Prospect Park, riffing “and thinking from an emo kind of place,” she said. She climbed atop a picnic table, imagining it was Elsa’s mountaintop, and “Let It Go” came to be.

The other nominated songs had equally intimate, and sometimes lo-fi, origins. Karen O, who has known and collaborated with Jonze for years, recorded “Moon Song” in the dining room of her apartment, with the wail of a fire truck audible on the track; Jonze used that demo in the movie trailer. The feel and instrumentation – a lullaby-esque love song strummed on ukulele – were inspired, she said, by a scene in the 1979 comedy “The Jerk,” in which Steve Martin and Bernadette Peters sing “Tonight You Belong to Me.” “It’s one of my favorite romantic moments in cinema,” she said.

For Williams, the musical phenom of 2013, with hits and Grammy wins in “Get Lucky” and “Blurred Lines,” his nominated song involved an unexpected songwriting battle: It took nine drafts to find the infectiously simple music and lyrics. “I was just challenged to go inward,” he said. “What does being happy feel like?” (If his performance on Oscar host Ellen DeGeneres’ talk show is any indication, expect his number at the ceremony to be an up-from-the-aisles dance-a-thon.)

U2 struggled, too, with the weight of writing about Nelson Mandela, a friend and an inspiration. “This was not a job for us,” Bono said in an interview Monday. “This was sort of a vocational moment, and we had to dig very, very deep.”

They were moved by his love letters and his statesmanship to write a melancholy romance that doubles as a political message. “We had very high hopes for this song,” Bono said. “When we came up with this, we thought, ‘We would shout it from the rooftops.’ And then the great man passed, and in fact we just sort of sat on the song. It would’ve been undignified to promote it.” The Oscar nomination, and performance, he said, “is our chance to serve that song.”

But Bono said he has no illusions about pitting “Ordinary Love” against “Let It Go.” “We’re likely to be left in the dust,” he said. (The category originally had another contender, “Alone Yet Not Alone,” from a little-seen movie of the same title, but the nomination was rescinded after the Academy decided promotional rules were broken.)