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Ben and Jen have a baby

Garner, Affleck enjoy congrats, but what's their daughter's name?
/ Source: Access Hollywood

Jennifer Garner and Ben Affleck welcomed a baby girl into the world Thursday, Access Hollywood has confirmed.

And when the news broke, the well wishes poured in from Hollywood.

"Congratulations," Charlize Theron said from the red carpet at her "Aeon Flux" premiere on Thursday night.

"That's fantastic," Courteney Cox told Access. "They are going to have the best time!"

And it looks like besides the well wishes, baby gifts are already on the stars' minds.

"I'm gonna send her some baby Sean John," Diddy said.

"That's awesome," Eva Mendes beamed. "Cute name too."

Actually Eva, the baby's name hasn't even been released yet. But that didn't stop several magazines from reporting the birth online hours before it happened.

The official time of the birth was 3:26 p.m. Pacific time.

But at 10:45 a.m. (Pacific time) on Thursday, Us Weekly was the first to report the birth long before it occurred, claiming an exclusive saying labor was induced Wednesday night and the baby's name was Violet, which is Jen's grandmother's name.

Us Weekly even quoted a source as saying "Ben was with her the entire time."

Well, where else would he be?

Within the hour, Star Magazine went with the story, quoting a source close to Affleck as saying "She's an absolutely beautiful and perfect little girl."

Too bad the baby hadn't been born yet.

The Enquirer reported that the baby arrived at 10 a.m. (Pacific time).

In reality, Ben and Jen's new bundle of joy arrived over five-and-a-half hours later.

The official line from the happy couple came to Access Hollywood when their spokespeople released the following statement:

"Mother, father and baby are doing great."

Ben and Jen tied the knot back in June in a secret ceremony in the Caribbean.

Dressed in a cream colored empire waist, straight gown with a sea-colored sash, the 33-year-old "Alias" star said her vows to 33-year-old Ben on the Carribean islands of Turks and Caicos.

Garner's "Alias" co-star Victor Garber officiated at the sunset ceremony.

The couple, who co-starred in 2003's "Daredevil," have been dating since August 2004. But except for occasional appearances together at Boston Red Sox games and low-key events, the couple have kept their relationship mostly out of the paparazzi limelight.

In January of 2004, Ben ended his very public relationship with Jennifer Lopez and the following March, Garner finalized her divorce from her husband of two-and-a-half years, actor Scott Foley.

This is the first child for both.

It was announced last month that Garner's ABC series, "Alias," will end its five-year run in May.