June was an exceptional month for Paramount Intl., with the studio’s overseas totals up a whopping 349% vs. the same month in 2010 — and with “Transformers: Dark of the Moon” scoring Par’s best-ever offshore start, at $219.8 million through July 3, this month looks to at least match the previous one’s boffo returns.Par, which was the first studio this year to reach $1 billion domestically, was greatly aided by stellar June players “Thor” and “Kung Fu Panda 2,” which so far collectively have grossed $639.1 million. While the majority of “Thor’s” $262.2 million tally was earned in May (the pic bowed day-and-date with the U.S. the weekend of May 6), “Kung Fu Panda 2″ launched mostly overseas throughout June, earning a big share of its $379.3 million total in that month. “Super 8″ also contributed to Par’s June boom, scoring much of its $46.3 million in the month. (That includes Japan, where the pic maintained the territory’s No. 1 spot over the July 1-3 weekend — its second frame — for a local cume of $11 million.) Last year, Par-DreamWorks Animation’s “Shrek Forever After” was the studio’s biggest summer player. But “Forever After” saw its biggest contributions, from Russia and the U.K., come during May and July, respectively. Australia was the only major territory to bow “Forever After” with enough time to earn significant June coin (pic bowed June 17). France and Germany both launched “Forever After” on June 30. “Dark of the Moon” should keep spirits high for Par after the film beat the studio’s previous foreign debut benchmark — $147 million, set by 2008′s “Indiana Jones and the Kingdom of the Crystal Skull.” “Dark of the Moon” also outperformed the previous “Transformers” installment, “Revenge of the Fallen,” by a commanding 51% during the film’s comparable Wednesday-Sunday debut frame. “Dark of the Moon” debuted in the top spot in all but one of its 58 markets, including South Korea, where the film scored the territory’s all-time biggest opening, with $28 million on 1,107 screens. Pic’s next-best market, Russia, contributed $22 million on 690 screens, followed by the U.K., where it grossed $16.5 million on 522. In both markets, 3D factored in significantly, with the film earning 75% and 70%, respectively, from the format. The 3D ratio for South Korea, however, at 53%, was less than even the U.S. (60%). Not surprisingly, 3D played a larger overall role overseas for “Dark of the Moon,” with 70%, than it did Stateside. That’s because overseas auds, particularly in Russia and most Asian markets, continue to embrace 3D, while interest in the format Stateside is waning. “Dark of the Moon’s” 3D version did perform well domestically, however. The pic’s 60% 3D opening share marks a much-needed improvement on the format’s previous perfs for pics like “Cars 2″ (40%) and “Green Lantern” (45%). In other territories, “Dark of the Moon” broke opening records — most likely boosted by 3D. Brazilian auds shelled out $5.9 million, making “Dark of the Moon” Par’s biggest opening in that country, while in smaller markets like Hong Kong and the Philippines, the pic posted best-ever opening figures. Hong Kong contributed $5.2 million; the Philippines, $4.8 million. Some European markets, including Spain and Italy, conceded their top spots to “Dark of the Moon,” but the film didn’t set the frame on fire, playing on par with — or slightly ahead of — “Revenge of the Fallen.” Spanish exhibs were skeptical whether “Dark of the Moon” would recover from negative buzz earned by the previous pic. (None of the “Transformers” pics have shown the same appeal in Spain as they have domestically.) A strong debut outing in those markets could ease some naysayers doubts, but “Harry Potter and the Deathly Hallows: Part 2″ launching in two weeks, doesn’t give much room for “Transformers” to grow. “Dark of the Moon” has two major countries, especially for 3D, yet to bow: China and Japan. Both markets will release the film this month. Emilio Mayorga in Barcelona, Ed Meza in Berlin, David Hayhurst in Paris, Nick Vivarelli in Rome and Mark Schilling in Tokyo contributed to this report.