CONGRATS KIM AND KANYE ON THE NEW BABY! TMZ Reports Kim Kardashian has given birth to a baby girl … TMZ has learned. Sources close to KK tell TMZ the baby and Kim are both in good health. We’re told Kim delivered the baby at Cedars-Sinai Medical Center this morning … 5 weeks early. Our sources say BF Kanye West was there for the entire thing — in the delivery room by Kim’s side. We’re told Kanye cancelled his appearance at his own record release party last night when Kim told him she was feeling “a little off.” It is the first child for Kim and Kanye.