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It's the third child for the 42-year-old 'Kill Bill
' actress, who has two children, Maya, 13, and Levon, 10, with ex-husband Ethan Hawke. It's also the third child for Arpad, who has two sons, Arpad Flynn Alexander, 14, and Aurelius Cy Andrea, nine, with ex-girlfriend and supermodel Elle Macpherson.
Uma Thurman with partner Arpad Busson. Credit: Getty Images
The couple, who have been dating on and off since 2007, announced they were expecting their first child together in February this year. According to an Us Weekly source, "Uma was definitely not planning on having another kid. It was a surprise... But she's over the moon about it, very excited."The star is believed to have given birth to their daughter on Sunday. No name has been confirmed as yet.Related Video: Top celeb-inspired baby names