Uma Thurman Appears At Lord & Taylor Fifth Avenue Flagship on November 9, 2011 in New York City. Credit: Thos Robinson/

Uma's a mama again!

Uma Thurman gave birth to a baby girl on Sunday, a source tells Us Weekly exclusively. No other info was immediately available. UPDATE: "Confirmed!" a rep for Thurman tells Us. "Mom and baby are doing well!"

It's the the third child for the 42-year-old Oscar nominee, who has two children -- Maya, 13, and Levon, 10 -- with ex-husband Ethan Hawke, and her first with financier beau Arpad Busson.

The Smash guest star and Busson, 49, called off their engagement in 2009, but reunited last year. "Uma was definitely not planning on having another kid. It was a surprise," a source told Us, which first broke new of Thurman's pregnancy back in February. "But she's over the moon about it, very excited."

Thurman and her daughter-to-be were feted at a small baby shower in NYC May 31 thrown by her half-sister Taya Thurman. Among the two-dozen guests at the baby pink-elephant themed bash were Thurman's Smash costars Debra Messing and Will Chase.

Thurman's ex-husband Hawke has also become a parent again following their 2004 divorce; the actor, 41, and second wife Ryan are parents to young daughters Clementine, 3, and Indiana, 11 months.