Kim and Kanye's Surrogate Out of Sight, But Still Sharing Pregnancy Progress

Kim Kardashian and Kanye West are in the homestretch for baby #3's arrival, and acting like the old pros they are in the birthing game ... even though this is their first time using a surrogate.

As we've reported, the couple's baby girl is due in January -- so, you might expect Kim and Kanye to be hovering around the surrogate mother almost constantly. Sources close to the couple tell us it's the exact opposite -- and, in fact, they don't see the woman much at all.

We're told they get regular medical updates on the surrogate and the bambino's health. So far everything's A-OK, and the word we heard repeatedly was "smooth."

People at Kim's baby shower say she's totally chill with the surrogate process.

As for the nursery ... Kim and Kanye were hands-on, and it will be shipshape for the baby's arrival at the Hidden Hills mansion.