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 (Saturday June 15th)... 5 weeks sooner than originally planned. Our sources say BF Kanye West was there for the entire thing. 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.