Uma Thurman and Arpad Busson when they started dating (Photo : Reuters)

 "Kill Bill" star Uma Thurman,42,  and her on-off boyfriend financier Arpad Busson , 49, welcomed their first child together -- a baby girl.

The baby girl makes three for the actress; Thurman has 10-year-old Levon and 13-year-old Maya with ex-husband Ethan Hawke.  The new baby is Busson's third child too; he has two sons, Flynn, 14, and Cy 9 , with his ex-fiancée, supermodel Elle MacPherson.

Thurman gave birth on Sunday and is said to be doing fine. "Mom and baby are doing well!" her rep told Us Weekly.

Thurman and Busson have been dating since 2007. They had a short break-up in 2009 after calling off their engagement but got back together that same year.

"Uma was definitely not planning on having another kid. It was a surprise," a source told the mag. "But she's over the moon about it, very excited."

Thurman and Busson announced the pregnancy in February, just before the actress made a guest appearance on NBC's "Smash." The mommy and baby-to-be celebrated a pink elephant-themed baby shower back in May in New York City. "Smash" costars Debra Messing and Will Chase celebrated with the actress and family. 

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