Welcome back, Paramount.After a three-month absence from the domestic box office race, the studio returns with “Paranormal Activity 4″ — the first of eight films from now through 2012, nearly triple any other studio — though early tracking suggests the serial scarer may be gripped a bit by franchise fatigue. “Paranormal 4,” which kick-starts Thursday with 9 p.m. sneaks, should land in the $35 million-$40 million range, based on pre-weekend estimates. That’s lower than the three-quel’s $52.6 million Stateside opening last year, but in line with the $40.7 million debut earned by “Paranormal Activity 2″ in 2010. It’s not unusual for top franchises to lose steam with later installments. And though horror films rely so heavily on opening weekend, Par and producer Jason Blum’s BlumHouse shingle have famously made the “Paranormal” films for peanuts. The fourth installment is no different, costing $5 million; even with marketing costs, the film should make a tidy profit. But will the studio’s stockpile of fourth-quarter pics be enough to lift Par in 2012 domestic market share ranking? The studio currently is in seventh place with $589 million domestically. While “Paranormal 4″ is expected to earn the bulk of this weekend’s global market share (pic bows day-and-date in 34 overseas territories including Australia, Brazil, Germany, Mexico, Russia, Spain and the U.K.), Summit’s James Patterson action adaptation “Alex Cross,” starring Tyler Perry and Matthew Fox, bows nationwide Friday, with three-day expectations ranging in the low-to-mid teens. “Cross” stands to benefit from the cross-section of Patterson and Perry fanbases. Pic, however, marks the first starring vehicle for Perry that he didn’t write and direct, which could limit some of the multi-hyphenate’s usual supporters. Paramount expects to attract die-hard scare-seakers to its late-night “Paranormal” screenings, leading up to the midnight shows. The early showtimes are meant to kick-start word-of-mouth through the weekend. “Paranormal 4″ marks the studio’s first release since music docu “Katy Perry: Part of Me” launched July 5. Before that, Par had only two other summer titles — “The Dictator,” which made $177 million worldwide, and “Madagascar 3,” the studio’s highest-grossing 2012 release, by far, with $681 million globally. The seven remaining Par pics include high-school comedy “Fun Size”; Denzel Washington starrer “Flight”; toon “Rise of the Guardians,” the last DreamWorks Animation film for Par; Tom Cruise pic “Jack Reacher”; and Christmastime entries “Cirque du Soleil: Worlds Away,” “Not Fade Away” and “The Guilt Trip.” Par enlisted “Paranormal” fans worldwide to vote to see the pic first via its “Want It” application on Facebook, mirroring the “Demand It” campaign it used to launch the original. With more than 250,000 votes counted, Par rewarded the top 25 cities (including Chicago, Los Angeles, Toronto, Mexico City, London and Paris) with free screenings Tuesday. The four-quel’s domestic playability should fall in line with the last two “Paranormal” pics. As a plus, Halloween — a sluggish moviegoing day — falls on a Wednesday this year. Summit’s soph-sesh scarer “Sinister” could distract the “Paranormal” aud. The holdover debuted with $18 million Stateside and should drop between 55%-65% this weekend. “Sinister” reached $20.7 million domestically through Tuesday. In limited release, Fox Searchlight launches Friday its Sundance award-winner “The Sessions” at four locations in New York and Los Angeles.