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Still, no official word on a name, or weight, or delivery details

(Photo: Josiah Kamau, BuzzFoto/FilmMagic)

STORY HIGHLIGHTS

Kim Kardashian and her boyfriend, Kanye West, are the parents of a newborn daughter
West, 36, first announced Kim's pregnancy in December, during a concert in Atlantic City
On her show, Kardashian revealed that she's having a girl

Finally, we have official confirmation!

On Sunday afternoon — aka Father's Day — grandma Kris Jenner tweeted "HAPPY FATHERS DAY @kanyewest !!!!!!"

Jenner's daughter Kim Kardashian gave birth to a daughter at Cedars-Sinai Medical Center in West Hollywood, Calif., according to E!, which airs her reality shows.

At Sunday's red carpet for the Daytime Emmys, Jenner called her grandchild "beautiful." Everyone, she said, is doing just fine.

Still no official name, weight, or delivery details, but at least those in the Kardashian inner circle are (sort of) speaking out. Of course, you can bet your cable TV subscription that everything involving the big reveal of this child is being, or has been, meticulously scripted. The Kardashians are nothing if not well-managed.

Family friend Jonathan Cheban Tweeted the following on Sunday: "Me and GRANDMA @krisjenner ..shes not too bad for having 3 grand kids! Hahahaha"

PHOTOS: : Kardashian, West go from new couple to parents

According to E!, network, papa West was by Kardashian's side for the delivery. The network also reports that the baby weighed in at under five pounds.

Kardashian hasn't tweeted about the birth; her publicist Jill Fritzo did not respond to numerous requests for comment. But Kim's sister Khloe tweeted this Sunday evening: "I can not even begin 2describe the miracle that is now apart of our family. Mommy/baby are healthy &resting. We appreciate all of the love." She continued: "More info will come when the time is right!"

PHOTOS: Relive Kardashian's maternity style

Meanwhile, congratulations are pouring in via Twitter.

Rachel Roy: So to welcome the sweetest lil angel into the universe, my niece blessings and love to @KimKardashian & KW xxRR

Russell Simmons: "There is no greater gift in life than a child's laughter! congrats to Kim And Kanye..."

Nas: "Congrats to Kanye 4 the birth of his daughter today too! To my bros w/ daughters!!"

Bethenny Frankel: "All kidding aside, congrats @kimkardashian on your baby girl. It's the most beautiful, best thing that could happen to you. Girls rule."

Us Weekly cites an unnamed hospital source as saying the reality star delivered "five weeks early. Kim got sick last night and had the baby early." E! confirms that the tot was born naturally.

The source added, "They're all doing great and amazing!"

It is the first child for the reality TV star and her boyfriend, West.

For those who have somehow been oblivious to the ongoing coverage of the Kardashian offspring, West, 36, announced Kardashian's pregnancy in December, during a concert in Atlantic City. "Stop the music and make noise for my baby mama … now you having my baby!" he shouted to the audience, which included Kardashian.

Since then, Kardashian, 32, has been a near-daily presence on blogs and websites, and in magazines, which have chronicled her unusual choices in maternity wear (consisting mostly of black and white pieces), her growing girth, and how much time she's been spending with West (not much). Their most high-profile public outing: May's Met Ball in New York City.

Kardashian told USA TODAY in March that she understood the interest in her. "I get that my life is very public and I live my life on a reality show. It gets a little tedious sometimes when I'm asked a bunch of questions that are so silly," she said.

Give this to Kardashian: she doesn't hold much back when she's on air. On the season premiere of her reality show Keeping Up with the Kardashians, she revealed that she's having a girl. "I'm so excited we're having a girl. Who doesn't want a girl? They are the best, and I know that's really what Kanye has always wanted. He wanted a little girl," she said.

Kim Kardashian and Kanye West are seen in Soho on May 6, 2013, in New York City. It's the rare photo of West smiling in public.(Photo: Raymond Hall, FilmMagic)

Of course, whether the child will be on the show remains up for debate. "I think, as of now, that's just, you know, a decision that Kanye and I made. … From the start, we're just gonna try to keep it as private as possible," she told Jimmy Kimmel in January.

In reality, her pregnancy has been chronicled on the show. On the season finale ofKourtney and Kim take Miami, she broke the news that she was having a baby. She had an opulent baby shower, with mom Kris Kenner, sisters Kourtney and Khloe, and West in attendance, which was filmed for the show.

West, whose public demeanor is surly at the best of times, was focused on his sixth album, Yeezus, which he was busy recording in Paris while Kardashian was pregnant and filming. The album, out June 18, already leaked online.

Meanwhile, Kardashian is, finally, a single lady. After a long battle that outlasted her 72-day marriage, Kardashian finally divorced basketball player Kris Humphries in April.

"I've said some things that I completely am, like, a hypocrite about now," Kardashian told Ryan Seacrest, one of the producers of her show, in an E! news special. "I would say things about Kourtney like, 'You cannot have a baby without being married!' "