The weekend B.O. will be carved up by family-adult counterprogramming bids as Disney-Pixar’s 13th animated feature “Brave” is projected to bow respectably alongside two modest R-rated newcomers: Fox’s “Abraham Lincoln: Vampire Hunter” and Focus Features’ “Seeking a Friend for the End of the World.”

“Brave,” which has the widest berth so far for a Pixar pic at 4,164 locations (including 2,790 3D), should range between $55 million and $65 million, according to pundits.

If “Brave” reaches the high end of those expectations, it’ll fit nicely among the top half of Pixar openings — nearest to “Cars 2,” which earned $66 million this same frame last year. Only four Pixar films — “A Bug’s Life,” “Toy Story,” “Toy Story 2” and “Ratatouille” — have earned less than $60 million during their first weekend of wide release.

“Abraham Lincoln,” on the other hand, may get stuck in the mid-teens rut that plagued “Rock of Ages” and “That’s My Boy” last weekend. And while there’s a potential low-$20 million-upside for “Lincoln” — at 3,106 engagements, of which 2,497 are in 3D — the film is still likely to trail “Bad Teacher,” which bowed this time last year at $31.6 million.

Focus is opening doomsday comedy “Seeking a Friend” at an aggressive 1,618 Stateside locations; the Steve Carell and Keira Knightley starrer, which cost a reported $10 million, is drawing tepid reviews and isn’t expected to hit double digits.

Disney kickstarted the overseas rollout for “Brave” earlier this week in key markets, including Australia, China and Russia. Fox’s 17-country spread for “Lincoln” this weekend includes only two major territories: Russia and the U.K.

Domestic tracking for “Brave,” budgeted at $185 million, has been solid among both genders, though females, especially moms, have a slight edge over male auds. Since “Brave” features Pixar’s first-ever female protagonist, Disney early on identified boys as a potential trouble spot, similar to the studio’s 2010 “Tangled.” But as with that film, the Mouse chose to focus heavily on the comedic and action elements of “Brave,” hoping to lure more interest from boys.

Set in medieval Scotland, “Brave” centers on a free-willed princess, voiced by Kelly Macdonald, who brings chaos to her kingdom after defying an age-old custom. Billy Connolly, Emma Thompson and Craig Ferguson co-star.

Fox, meanwhile, should attract a mostly adult audience for the $69 million-budgeted “Vampire Hunter,” the studio’s second R-rated summer tentpole after “Prometheus.”

“Vampire Hunter,” from helmer Timur Bekmambetov and staring Benjamin Walker, could attract fans of author-scripter Seth Grahame-Smith’s source novel. Fox has been marketing aggressively the film’s action sequences, with hopes that 3D also will help drive weekend filmgoing.

At the specialty B.O., Sony Pictures Classics launches Woody Allen’s “To Rome With Love” at five locations in New York and L.A.

Aside from its “Seeking a Friend,” Focus continues to broaden boffo specialty player “Moonrise Kingdom” into 394 Stateside locations, up from 178 last weekend. Entering its fourth frame, “Moonrise” has cumed nearly $8 million domestically.