Relativity Media saw its best opening to date in a generally soft sesh as Bradley Cooper starrer “Limitless” topped the weekend’s domestic box office with an estimated debut perf of $19 million from 2,756 locations.

Pic was even further ahead of its competitors than B.O. pundits had expected, since “The Lincoln Lawyer” and “Paul” had been tracking similarly, according to pre-release market data. The weekend was down 11% from the same frame last year.

Lionsgate made headlines with a rare ticket discount offer for “The Lincoln Lawyer,” selling ducats for $6 and even $1 from online discount service Groupon. Based on the Michael Connelly mystery novel, “Lawyer” played just above studio expectations, scoring an estimated $13.4 million at 2,802 playdates. According to Lionsgate, 190,000 tickets were sold using Groupon’s discounted rate, though only 40,000 of them were redeemed during opening weekend. Grosses were tallied at the full ticket price, with discounts reportedly allocated through the P&A budget.

R-rated alien laffer “Paul” trailed slightly behind, with a projected $13.2 million at 2,707.

Neither “Lawyer” nor “Paul” could top holdovers led by Paramount’s “Rango” and Sony’s “Battle: Los Angeles.”

“Rango” dropped a mere 32% in its third frame for an estimated $15.3 million, followed by “Battle,” down 59% to an estimated $14.6 million. “Rango” has cumed $92.6 million; “Battle,” $60.6 million.

The pair of holdovers played best overseas for the second straight week, though this weekend “Battle” won bragging rights, with $29 million from 55 markets, compared to “Rango’s” $20 million international take in 54 territories. The two titles have proven their potency with overseas auds as “Rango” reached $73 million internationally and “Battle” nearly $52 million.

In limited Stateside release, Fox Searchlight’s “Win Win” got off to a fine start, scoring a per-screen average of $30,723 from five locations in New York and L.A. The Tom McCarthy-helmed indie, with an estimated weekend gross of $153,615, marks the best bow for McCarthy, whose 2008 pic “The Visitor” opened to $86,488 at four locations, averaging $21,622 per screen.

“This isn’t a sprint, it’s a journey,” said Searchlight exec VP of distribution Sheila DeLoach. “But word of mouth is on our side.”

Meanwhile, more specialty auds turned out for Focus Features’ “Jane Eyre,” which successfully expanded to 11 new markets in its second outing. Period pic tallied a strong $18,377 per-screen average from 26 runs, up from four last weekend. To date, “Jane Eyre” has the year’s highest opening per screen average for a traditional theatrical release (Kevin Smith’s “Red State” roadshow tallied high averages with live theater-sized ticket prices.)

“Limitless” scored a fine overall B+ CinemaScore rating that was driven by moviegoers over 25.

“Everyone thought it was going to be a three-way race, and for us to win by a wide margin is proof that we played broadly,” said Kyle Davies, prexy of theatrical distribution for Relativity. “The CinemaScore and positive word of mouth says that (the film) has playability.”

“Limitless,” only the fourth solo release for Relativity and its third fully produced title (December release “The Warrior’s Way” was a service deal for Relativity), turned in a much better perf than its previous two 2011 titles, “Season of the Witch” and “Take Me Home Tonight.”

Distrib’s newest release also epitomizes the company’s frugal approach. “Limitless” cost around $30 million, but with foreign pre-sales and tax rebates, Relativity is responsible for less than $1 million of the total production cost.

Pic’s weekend perf, boosted by appeal for Cooper and Robert De Niro, puts it on track to become a profitable venture for Relativity, even with marketing costs added to the equation. As part of Relativity’s ad scheme, the company employed various online strategies to increase awareness for the film, including a mock pharmaceutical drug sale that advertised the “smart drug” in the film.

Directed by Neil Burger from a script by Leslie Dixon, “Limitless” tells the story of a struggling writer who discovers a drug that maximizes his brain potential. Pic is based on author Alan Glynn novel “The Dark Fields.”

Appealing to a mostly adult aud, U’s R-rated “Paul” should be profitable in the end, with overseas grosses already totaling $28.1 million. The Working Title production bowed early in the U.K. and France to benefit from local popularity for Brit thesps Simon Pegg and Nick Frost. “The picture was made with an eye for the international audience,” said U distrib topper Nikki Rocco.

Pic’s domestic playability — the film scored a B+ CinemaScore — could continue throughout the coming weeks, especially since it’s the newest adult comedy until U’s “Your Highness” on April 8. “Paul” expands into 53 more territories in the next few months.

Lionsgate’s $40 million “Lincoln Lawyer” played slightly better than “Paul,” with the Groupon promotion helping draw attention. Lionsgate distribution exec David Spitz described the Groupon promotion as “trying to market our film to break through the clutter.”

According to Lionsgate, 89% of auds who redeemed their Groupons this weekend hadn’t planned on seeing the film until they saw the discount offer. “The key to the promotion was to get the word out,” Spitz said. “Now, on Monday, they’ll tell a friend, and so on.”

Just over one-fifth of Groupon buyers redeemed their tickets this weekend. Groupon ticket sales aren’t collected until after moviegoers redeem their ticket at theaters, which include all partners of online ticketing service Fandango (i.e., major circuits like Regal and some AMC plexes).

Like soph entry “Battle,” both Warner Bros.’ “Red Riding Hood” and Disney’s “Mars Needs Moms” landed in the top 10 during their second outing. “Red Riding Hood” fell 48% for an estimated weekend take of $7.3 million, while “Mars Needs Moms” was down 23% with $5.3 million.

“Red Riding Hood” has totaled $26 million domestically, with an additional $5.6 million from overseas grosses. “Mars Needs Moms” reached $15.4 million at Stateside plexes; foreign tally stands at $7.8 million.

At the specialty B.O., Sony Pictures Classics bowed Dutch-lingo pic “Winter in Wartime,” with a so-so per-screen average of $5,386 at three U.S. locations. Weekend total was $16,157.

Meanwhile, Anchor Bay Films did well with indie title “Kill the Irishman,” which played at a broadened 21 engagements and averaged an estimated $6,842. In its second week, pic has grossed $335,698, a fine start for limited play.

Gotham’s Metropolitan Opera continued its fifth season of live transmissions on Saturday, screening Donizetti’s “Lucia di Lammermoor” for an estimated $2.2 million in North America. It was seen live on more than 850 screens, with an additional 425 screens in 26 European markets and eight in Latin America.