And baby makes “III.”

Tom Cruise was popping up all over Europe last week, arriving via helicopter and hopping barricades to meet fans while talking up his latest pic — despite earlier assertions he’d cut short his Euro tour to go home to fiance Katie Holmes and their new child.

It turns out this is a Suri with a fringe … benefit.

The new tyke has been Cruise’s best promotional tool for “Mission: Impossible III,” as virtually every major Euro media outlet mentioned her in its coverage of Cruise and the film.

In Rome on April 24, the actor said that would be his only European stop. But he popped up the next day at the London preem, telling the press that Holmes and Suri didn’t mind him staying another night.

When he hit Paris on April 26, he played the proud papa again — this time to dodge a press conference outside the Ritz. His spokeswoman said he was off to the city to spend time with his other children, Isabella and Connor.

He also went shopping for — what else? — baby clothes.

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In his whirlwind Euro jaunt, Cruise generated plenty of publicity for “M:I3” — and some odd riffs on baby Suri’s name.

France’s RTL surprised ayem listeners with news that “Tom Cruise’s wife recently gave birth to a little mouse.” The anchor then spelled out the name of “S.U.R.I.” — otherwise indistinguishable from “souris,” Gallic for mouse.

Proving that you can never be too careful when naming your child, the name reportedly also means “pickpocket” in Japanese and “go away” in Hebrew. And then there’s the name’s resemblance to Surrey — the U.K. birthplace of Scientology founder L. Ron Hubbard.

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Apart from the Cruise promo machine, UIP has a secret weapon to boost “M:I3”: an outdoor campaign featuring sparkling London buses.

Viacom Outdoor has customized a fleet of 30 red buses with a sequenced lighting effect. LED bulbs on the sides of the buses are programmed to light up in a pattern tracing the outline of the film’s logo.