When the directors yelled, “That’s a wrap” on the sets of “Brokeback Mountain” and “Capote,” the work was just beginning for Heath Ledger and Philip Seymour Hoffman in their quests for Oscar glory.

Ever since each film won acclaim at festivals in September, each actor has been running a breathless, worldwide campaign to keep his name on the minds of Oscar voters.

Every word they said, every red carpet they walked, every shiny doodad they hoisted at every podium became a factor in how their peers back in Hollywood perceived their worthiness to win the only award that matters.

Then one of the actors stumbled and the surewinner was all but decided – way back in January.

From the start, Ledger wasn’t free to focus on the Oscar quest. On Oct. 28, he and his girlfriend had a baby, Matilda Rose.

“Any hype or excitement around work doesn’t mean anything,” he said later. “Having this child has taken any pressure off my shoulders . . . It doesn’t matter.”

All of the nominated actors – including David Strathairn (“Good Night, and Good Luck”), Joaquin Phoenix (“Walk the Line”) and Terrence Howard (“Hustle & Flow”) – earned raves from critics. But Ledger and Hoffman seemed to transform themselves so completely they made it a two-man race from the start.

As the critical praise came in, the studio machines geared up, blitzing trade publications with ads and organizing screenings and parties for members of the Academy of Motion Picture Arts and Sciences.

Once sniffed at with disdain, Bob and Harvey Weinstein’s shameless spending sprees on awards politicking are now de rigueur in Hollywood. And the Weinsteins proudly point out the 220 Oscar nominations they brought to Miramax with relentless marketing.

By pushing mediocre product, such as 2000’s English-language version of “Chocolat,” onto the list of nominees, the Weinsteins proved that Oscar voters are like cola drinkers: They choose the one they’ve heard a lot about.

The Ledger-Hoffman battle began in earnest at the Toronto Film Festival – where “Brokeback” made its premiere – in September. Both actors attended, though Ledger looked sterling, especially when “Brokeback” took top prize at Cannes the same week.

Later that month, Hoffman showed up at the New York Film Festival to promote “Capote,” though it wasn’t the opening-night feature. On Nov. 2, Hoffman even showed up at the “MTVu Woodie Awards” at Roseland Ballroom, which would only be cable-cast to college students.

On Dec. 12 and 13, with “Brokeback” dominating critics’ best picture awards, Ledger was named winner of the New York and San Francisco Film Critics’ awards for Best Actor. A few days later, he told USA Today a poignant story about a gay uncle who was forced to come out to his father at age 20. Heartbreaking stuff, and completely on-message for Oscar.

But on Jan. 8, Ledger didn’t show up at the New York Film Critics Circle dinner to claim his award. He sent a note saying he was in Australia introducing his new baby to friends and family.

Since winners were announced in advance, Hoffman knew he wouldn’t win anything that night, but graciously showed up anyway to praise his “Capote” colleagues: director Bennett Miller and screenwriter Dan Futterman. The next day, Ledger was a no-show again in Santa Monica at the Critics’ Choice Awards. He lost to Hoffman, who gave a humble speech: “I’m not the easiest guy to work with,” he said.

The tide had begun to turn in Hoffman’s favor.

Meanwhile, in an interview Ledger blasted some Utah theaters that declined to show “Brokeback Mountain,” saying, “I heard a while ago that West Virginia was going to ban it but that’s a state that was lynching people only 25 years ago. So that’s to be expected.”

Dissing West Virginia isn’t going to hurt you much in Hollywood, especially if you’re championing gays, but still: crabby, very crabby.

Hoffman stuck to the topic in his interviews: the character, his hard work, his gratitude. On Jan. 16, Hoffman captured the Golden Globe award as Ledger looked on.

“I was given the best part of my life, basically, and I know that,” Hoffman said gratefully.

On Jan. 29, Hoffman clinched it at the Screen Actors Guild Awards.

Ledger and Gyllenhaal, at the podium to introduce their film for Best Ensemble, put on an amateurish performance that some read as a gay minstrel show. Ledger stood with a hand on his hip as the two of them smirked and giggled their way through the introduction, which attempted to earnestly explain the appeal of the film.

Ledger had strayed far from the message: He seemed to be sending the idea that he was embarrassed to be associated with a gay movie. At best, he looked unprofessional for mocking the broadcast’s writers.

In the last two weeks of the race, with Oscar ballots due at the end of February, Ledger blundered again at the Berlin Film Festival. He told a press conference George Clooney deserved to win Best Supporting Actor – dissing his co-star Gyllenhaal.

Ledger also seemed irritated by the Oscar race: “We’re all just being dragged through it,” he said. Grouchy, definitely grouchy.

Hoffman’s take was exactly the opposite; he told reporters that “One of the great things [about being nominated] is getting to know a bunch of other actors.”

At Hoffman’s own appearance in Berlin he stuck to the script, refusing to comment on his chances and talking instead about “Capote” and Capote: “When you’re playing a character, I think you have to … try to put judgment aside,” he said.

Two days later, Hoffman made a perfectly timed appearance on “60 Minutes” to talk about his battle with drug addiction. Again, a stellar move in appealing to Hollywood’s recovering anything-holics.

That same night, the British press sniped at Hoffman after his Bafta (British Oscars) win. In his acceptance speech, he addressed his girlfriend, Mimi O’Donnell: “I want to say I love her and she looks really hot.” That prompted a Guardian scribe to carp about “the faintly queasy spectacle of . . . Hoffman trumpeting his hetero credentials.”

But simply being heterosexual isn’t (yet) enough to crash your career in Hollywood.

Going into tonight’s Oscars, Hoffman is the single biggest favorite. Don’t bet against him.

kyle.smith@nypost.com

PERFORMANCE BY AN ACTOR IN A LEADING ROLE

Philip Seymour Hoffman – Capote

Terrence Howard – Hustle & Flow

Heath Ledger – Brokeback Mountain

Joaquin Phoenix – Walk the Line

David Strathairn – Good Night, and Good Luck

PERFORMANCE BY AN ACTRESS IN A LEADING ROLE

Judi Dench – Mrs. Henderson Presents

Felicity Huffman – Transamerica

Keira Knightley – Pride & Prejudice

Charlize Theron – North Country

Reese Witherspoon – Walk the Line

RACE FOR BEST ACTOR

HOFFMAN – 15% chance of winning

Sept. 10: Attends Toronto Film Festival

Sept. 27: Speaks at New York Film Festival, even though “Capote” isn’t opening night feature

Jan. 9 & 15: Wins Best Actor at Critics’ Choice Awards, Golden Globes

Jan. 29: Wins Best Actor at Screen Actors Guild Awards

Jan. 31 Oscar nominations announced

Feb. 17: Sticks to the script in Berlin

Feb. 19: Makes perfectly timed appearance on “60 Minutes”

LEDGER – 80% chance of winning

Sept. 10: “Brokeback” premiers at Toronto Film Festival, wins tops prize at Venice Film Festival

Oct. 24: Has new baby, Matilda Rose, with girlfriend Michelle Williams (right)

Dec. 12 & 13: N.Y. and S.F. Film Critics name him Best Actor

Dec. 15: Tells USA Today moving story about gay uncle

Jan. 8 & 9: Skips N.Y. Film Critics Circle dinner and Critics Choice Awards

Jan 10: In Sydney Herald, blasts West Virginia theaters that banned “Brokeback”

Jan 29: Makes possibly homophobic speech for “Brokeback” at SAG Awards

Feb. 15: Tells Berlin press that George Clooney (below) deserves to win Supporting Actor Oscar, not co-star

Gyllenhaal