Kim Kardashian's baby daughter weighed just 4lb 15oz.

The socialite's child North West - her first with partner Kanye West - was born around five weeks prematurely on June 15 at Cedars-Sinai Medical Center in Los Angeles, California, and the tot didn't even make 5lb because she was early.

Despite being small in size, the baby - nicknamed ''Nori'' - is ''perfect'' and ''looks just like Kim - with her dark hair and some of her features'', a source told Us Weekly magazine.

Kim, 32, and Kanye, 36, were very worried when the 'Keeping Up with the Kardashians' star went into labour early but doctors at the hospital assured the couple there was no need to fret.

A source said: ''Kim was scared. The doctors had to assure her that, even though the baby was early, she was ready.''

After a week-long stay at the hospital, Kim was given the all-clear to leave with her baby last weekend and the trio are staying with Kim's family at their Bel Air mansion until renovations on their new home are completed.

Although Kim is getting help from her mother Kris Jenner, she is a hands on mother and is breastfeeding Nori and loves changing her nappy.

A source revealed: ''The family is going to wait on Kim hand-and-foot and do everything around the house while she and Kanye just chill with the baby.''