Will the third time be the charm for “Family Guy”?

Fox is betting its animation supremacy — or, as its marketing team has coined it, the net’s “animation domination” — on the return of the cult fave.

With critically lauded skein “King of the Hill” near the end of its lifespan and “The Simpsons” showing signs of age (although still a force after 350 episodes), the future of Fox’s Sunday night, not to mention News Corp.’s track record of successful primetime toon laffers, centers on the show.

“We believe, until we’re proven wrong on Monday morning, that the return of ‘Family Guy’ is an event,” says Preston Beckman, Fox’s exec VP of strategic program planning.

“Rather than trying to come up with stunts or specials for Sunday in May sweeps, the best thing we could do was take our brand — ‘The Simpsons’ and ‘King of the Hill’ — and use it to create a night of animation that will make the return of ‘Family Guy’ even bigger.”

It’s become animation lore: Fox launches “Family Guy” after the Super Bowl in 1999; show thrives after “The Simpsons” but struggles after moving to Tuesday nights. Gail Berman joins the net and revives the show, which dies a second time after airing in an even tougher Thursday slot.

This time out, Beckman believes the net finally got it right. “Family Guy” will be paired with the new “American Dad,” both of which come from creator Seth MacFarlane.

That satisfies two of the cardinal rules of primetime animation: The best show to pair with an animated comedy is another animated comedy. (“King of the Hill” hit its peak behind “The Simpsons,” after all.) And the animated comedies that work best? Shows about human families.

That was true in the 1960s (“The Flintstones” and “The Jetsons”) and it’s true now.

“That’s why ‘Simpsons’ and ‘King of the Hill’ had the success they did,” Beckman says.

Sked may rep Fox’s best shot at regaining ground, particularly among young men, on Sundays. Once Fox’s strongest night, Sunday has been a tougher nut for the net to crack since “The X-Files” disappeared in 2002.

“King of the Hill” lost some of its mojo after Fox relegated the show (about to hit 200 segs) to the unenviable 7 p.m. slot. “Malcolm in the Middle” hit some growing pains after star Frankie Muniz grew up. And “Arrested Development” earned heaps of praise over the past two years — just not from viewers.

This season, up against ABC’s suddenly hot perf on the night, Fox saw its fortunes dip even more.

“Sunday is such a tough night, between ABC taking over the night and the fact that there are so many more disruptions and stunts on the night,” Beckman notes.

Hence the net’s decision to rely on a genre it knows better than any of its broadcast brethren.

While rivals have taken several shots at creating their own animated hit (most recently, NBC’s short-lived “Father of the Pride”), only Fox, which jumpstarted the form in 1989 with “The Simpsons,” has made it work.

Homer and family remain strong players for Fox, and have weathered the net’s roller-coaster ride for an astonishing 350 episodes.

“In terms of number of episodes, it’s second (among comedies) only to ‘Ozzie and Harriet,’ ” notes “Simpsons” exec producer Al Jean. “You see shows that get a lot of attention for a year or two, and people tend to forget a show that has run as long as ‘The Simpsons.’ ”

Of course, even “The Simpsons'” ratings declined this season. And at some point, the show will have to end its run.

But that’s still in the distant future. Jean notes the “Simpsons” voice cast is signed through season 19, which would put the show at about 430 episodes.

“Then the temptation might be to go to 20 seasons,” Jean adds.

The show long ago became the gold standard for how corporate parent News Corp. can exploit a successful animated series — and how, given the fact the characters never age, a boffo animated laffer can last seemingly forever.

That’s why “animation domination” isn’t just a Fox tagline; it’s a financial strategy.

“It’s extremely important for this corporation,” Beckman says. “The upside of returning ‘Family Guy’ in a positive way is enormous for this company, as ‘The Simpsons’ has been all of these years.”