‘Specialist,’ ‘Pulp’ Duke It Out Over No. 1 Spot : Box office: Distributors battle over weekend gross estimates for the heavily advertised films. ‘Wes Craven’s New Nightmare’ takes third place.

Depending on whose version proves accurate, Quentin Tarantino’s new film, “Pulp Fiction,” starring John Travolta and Bruce Willis, was either the weekend’s top-grossing film or the runner-up.

On Sunday, Miramax, which released the film, was engaged in a my-gross-is-bigger-than-yours contest with Warner Bros. The latter distributor claimed its movie, “The Specialist,” starring Sylvester Stallone, was outselling “Pulp Fiction” and was still No. 1 in its second weekend.

Most estimates had the Miramax release taking in $8.4 million to $8.6 million. But Miramax was claiming $9.16 million on 1,338 screens. The lower figures for “Pulp” supposedly didn’t include 72 theaters, mostly in Canada, that Miramax had neglected to mention earlier. An oversight, said Bob Weinstein, who along with his brother Harvey, runs Miramax.

That led Warner distribution chief Barry Reardon to respond, “Give me a break” and to increase his “official” $8.9-million estimate for “The Specialist” to an unofficial $9.3 million to $9.4 million. Weekend figures released Sunday are imprecise estimates made while box offices are still open, but are based on typical ticket-sale patterns.

John Krier of Exhibitor Relations, Inc., a firm that tracks box-office performance, expressed skepticism about Miramax’s figures.

But Weinstein stood firm, saying, “Anybody is welcome to come in here and check it out if they like.”

What is beyond dispute is that Miramax and Warner Bros. both advertised heavily to attract weekend audiences. Miramax competitors are claiming that the company spent well in excess of the $5 million reported to open the film. “In that ballpark” was as specific as Weinstein was willing to get.

Regardless of the final gross, the Tarantino film’s debut was notable in that it indicated break-out potential for the $8-million production. According to industry sources, “Pulp” performed well in all markets save for small cities. However, business was up only 27% from Friday to Saturday (box-office grosses can rise as much as 50% on a second day) simply because most houses were sold out, Weinstein said. But one competitor said “Pulp” was flat from Friday to Saturday.

The true test will be whether the film has enough pulp to sustain by word of mouth after the costly opening-week ad blitz.

Coupled with the more than palatable opening performance of another independently made film, New Line’s “Wes Craven’s New Nightmare” which grossed about $7.1 million on 1,850 screens (and finished in third place), the major studios got a little run for their box-office share over the past weekend. (The term “independent” is a loose one. Miramax is owned by Disney, New Line by Ted Turner). Considering that it’s the seventh installment in the “Nightmare” series, that was a pretty good showing, said Mitch Goldman, New Line’s president of marketing and distribution.

Overall, business for the weekend was no better and no worse than last year. Regardless of its box-office standing, “The Specialist” dropped more than 30% from its $14-million opening plateau with the added competition of “Pulp” and “Nightmare.”

Other weekend openings were less notable. The kid comedy “Little Giants” wasn’t gigantic with about $5.4 million on more than 2,000 screens. Savoy Pictures’ “Exit to Eden” was out the door with little more than $3 million in 1,670 theaters. The likable “I Like It Like That” surfaced in 55 theaters with little hoopla (but some decent reviews). It was not enough to lift it past $250,000. The new version of “The Browning Version” played old with only $44,000 on 12 screens.

Among the returning films, “The River Wild” drew $5.5 million in its third weekend. “Only You” got in an acceptable second weekend of $4.3 million and has grossed almost $12 million in 10 days.

And the indomitable “Forrest Gump” just keeps rollin’ along. The year’s top-grossing film should also be one of the best fall performers with $3.3 million over the weekend for seventh place and $280 million to date.

Ninth was “The Shawshank Redemption” with $2.5 million, and 10th was “Quiz Show” with $2.3 million.