When Kim Kardashian was admitted to Cedars-Sinai Medical Center in Los Angeles on June 14, she didn't realize the harrowing night ahead of her. Due to complications, Kardashian - whom was about 37 weeks pregnant - went into premature labor.

Kardashian and her boyfriend of 16 months, Kanye West, 36, spent the night in the hospital, awaiting the birth of their firstborn.

In the new issue of People Magazine, sources detail the "emotional" evening, as West rushed to her side.

By the next day, Kardashian had given birth to a girl, "the prettiest, tiniest thing with a full head of straight, dark hair, a cute little nose and Kim's lips," a family friend said. "She's already smiling!"

The couple's baby girl has been spending time in an incubator to regulate her body temperature, a standard course of treatment for premature babies and is "doing very well," says a hospital source.

The new parents are over the moon -- and are close to picking a name for "Baby K."

Rumors have swirled that Kardashian and West have named their daughter, Kaidence Donda West. The couple have yet to confirm the baby's name.

Model Brittny Gastineau, a longtime pal of the pair, gushed about the baby.

"I've been there every day," Gastineau told Us Weekly of visiting the new mom, adding that Kardashian and her rapper beau are naturals.

"It is not weird at all [to see them as parents]. Everything is normal...It's all meant to be. They have been amazing," she said.

Khloe Kardashian tweeted shortly after her niece's birth, revealing: "I cannot even begin 2 describe the miracle that is now a part of our family. Mommy/baby are healthy & resting. We appreciate all the love."

Added Kardashian matriarch Kris Jenner on the red carpet at the Daytime Emmy Awards: "It all happened so fast. They're doing well."

"We are all good and extremely happy and thrilled for the new baby," she gushed to Showbiz Tonight. "She's doing great and beautiful. So very exciting.

Tags: Kim Kardashian Kanye West