
From Keith Urban's publicist:
"Nicole and Keith Urban are delighted to announce that Nicole Kidman gave birth to a baby girl on Monday morning, July 7, 2008, in the United States. Sunday Rose Kidman Urban weighed 6 pounds, 7 1/2 ounces. Husband Keith was by Nicole's side and mother and baby are very well."
Urban's post to his web site upon the baby's birth:
“Earlier this morning Nic gave birth to our beautiful baby girl, Sunday Rose Kidman Urban.
“We want to thank everybody that has kept us in their thoughts and prayers. We feel very blessed and grateful that we can share this joy with all of you today.”
The Australian actress has spoken publicly of her desire for biological children since she divorced Tom Cruise. Kidman recently told Vanity Fair that she had a miscarriage early on in her relationship with Cruise, leading them to adopt. It has also been reported that Kidman suffered an ectopic pregnancy while married to Cruise.
After marrying native New Zealander Urban in 2006, Kidman stated: "I think I would be very sad if I wasn't able to have a baby. Keith knows I want one, and he has been getting there slowly."
The baby is the first for Kidman and Urban, who married in June 2006. She has two children, Isabella, 15, and Connor, 13, with Cruise.
Cruise filed for divorce in February 2001 after 10 years of marriage, citing irreconcilable differences. The divorce was finalized later that year.
Kidman, 41, won an Oscar for her role in the 2002 film "The Hours."
During a concert Saturday in Nashville, Urban said, "I'm going to dedicate a song to my very, very, very, very, very pregnant wife" before singing his hit, "Better Half."
Urban, 40, won a Grammy in 2006 for best male country vocal.
"The unknown excites me a lot," Urban told reporters in May. "What kind of feelings will fatherhood bring? I'm sure I can't even imagine, but I am really looking forward to finding out
The couple, who were both raised in Australia, have a home in Nashville.
UPDATE March 12, 2012:

This photo of Nicole Kidman, Keith Urban and their daughters, Sunday Rose and Faith Margaret, at the Sydney airport on Wednesday was posted on the entertainment website, Popsugar.
Nicole Kidman and daughter Sunday Rose
UPDATE-- Official announcement from Nicole's publicist:
Nicole Kidman has delivered her first child, a baby girl, her agent, Wendy Day, said.
Sunday Rose Kidman Urban was born in the American country music capital of Nashville just before midnight on Monday Eastern Australian standard time, weighing 6 pounds 7.5 ounces (2.93 kilograms).
Her husband, Australian country singer Keith Urban, was by her side for the birth and mother and baby are very well, Ms Day said.
The couple had just celebrated their second wedding anniversary in Nashville where they have been living in a gated community. They were married in Manly on June 25, 2006.
The Academy Award-winning actress has two adopted children - 15-year-old Isabella Jane Kidman-Cruise and 13-year-old Connor Anthony Kidman-Cruise - with her previous husband, Tom Cruise.
From the UK Times Online: 50 craziest celebrity baby names (in alphabetical order)
50 craziest celebrity baby names (in alphabetical order)
Aanisah: Macy Gray (also mother to Tahmel)
Apple: Chris Martin and Gwyneth Paltrow
Astrella Celeste: Donovan and Linda Lawrence (also parents to Oriole Nebula)
Atherton Grace: Don Johnson and Kelley Phleger
Audio Science: Shannyn Sossamon
Aurelius Cy: Elle Macpherson and Arpad Busson
Blue Angel: U2's The Edge and Aislinn O'Sullivan
Bluebell Madonna: Geri Halliwell
Brooklyn: David and Victoria Beckham (also parents to Romeo and Cruz)
Calico: Alice and Sheryl Cooper (also parents to Sonora Rose)
Camera: Arthur Ashe and Jeanne Moutoussamy
Destry: Steven Spielberg and Kate Capshaw
Diezel Ky: Toni Braxton and Keri Lewis (also parents to Denim Cole)
Fifi Trixibell: Bob Geldof and Paula Yates (also parents to Peaches and Pixie)
Fuchsia: Sting and Frances Tomelty
Gaia: Emma Thompson and Greg Wise
Gulliver: Gary Oldman and Donya Fiorentino
Heaven: Lil' Mo (also mother to God'Iss Love Stone)
Heavenly Hiraani Tiger Lily: Paula Yates and Michael Hutchence
Hopper: Sean Penn and Robin Wright
Ireland: Alec Baldwin and Kim Basinger
Jaz: Steffi Graf and Andre Agassi
Jazz Domino: Joe Strummer
Jermajesty: Jermaine Jackson and Alejandra Genevieve Oaziaza (previously married to Jermaine's brother Randy)
Kal-El Coppola: Nicholas Cage (Kal-El is Superman’s original birth name)
Kyd: David Duchovny and Tea Leoni
Lark Song: Mia Farrow and André Previn
Lennon: Liam Gallagher and Patsy Kensit
Liberty: Ryan Giggs
London Emilio: Slash
Luna Coco Patricia: Frank Lampard and Elen Rive
Marquise: 50 Cent
Memphis Eve: Bono
Moon Unit: Frank Zappa, also father to Dweezil and Diva Muffin
Moxie CrimeFighter: Penn Jillette (also father to Zolten)
Ocean: Forest Whitaker (also father to Sonnet and True)
Pilot Inspektor: Jason Lee and Beth Riesgraf
Poppy Honey: Jamie and Jules Oliver (also parents to Daisy Boo)
Rocket: Robert Rodriguez (also father to Racer, Rebel and Rogue)
Rufus Tiger: Roger Taylor also father to Tiger Lily and Lola Daisy
Saffron Sahara: Simon and Yasmin Le Bon (also parents to Amber Rose and Tallulah Pine)
Sage Moonblood: Sylvester Stallone and Sasha Czack (also parents to Seargeoh)
Satchel: Spike Lee and Tonya Lewis Lee
Seven Sirius: Andre Benjamin and Erykah Badu
Shiloh Nouvel: Brad Pitt and Angelina Jolie
Sosie: Kevin Bacon and Kyra Sedgwick
Suri: Tom Cruise and Katie Holmes
Tallulah: Bruce Willis and Demi Moore (also parents to Scout and Rumer)
Willow Camille Reign: Will Smith and Jada Pinkett-Smith
Zola Ivy: Eddie Murphy and Nicole Mitchell
http://www.vizu.com/poll-vote.html?n=104427
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