celebrity kids

Three Kardashian baby daddies are all taking a leap of faith ... that their baby mamas will give them proper custody and/or visitation without the benefit of a custody agreement.

Sources connected to all three men tell TMZ, they never papered their financial and custodial arrangements. We're told Travis Scott and Kylie don't have anything in writing regarding custody or support of their newborn daughter. Same goes for Tristan Thompson and Khloe Kardashian, although that may be a bit premature since she hasn't given birth.

More interesting, perhaps, is that we're told Scott Disick doesn't have a written custody agreement with Kourtney Kardashian. They have 3 kids and from what we hear, the only conflict involves Scott's sobriety.

They have the option at any time of trying to ink a custody arrangement or going to court for one if they can't do it on their own.

Kourtney Kardashian was holding on to her dear life in NYC ... her dear life named Penelope.

Kourtney's mommy & me day with Penelope in Central Park Sunday also included North West. They skated to "Redbone" by Childish Gambino and then took a walk under some light rain. It was quite the escape from L.A. where it was a steamy 81 degrees.

Kourtney's really getting the hang of this ice skating thing. But more than that, she's totally nailing the part of kool mommy and fun auntie.

Kylie Jenner and Travis Scott are parents after she gave birth Thursday to a "beautiful and healthy" baby girl ... according to Kylie herself.

Kylie made the announcement Sunday. She delivered her firstborn at Cedars-Sinai in L.A., the same hospital where sisters Kim and Kourtney delivered their broods. Rob's daughter, Dream, was also born there. Kylie's kid came out at 4:43 PM weighing 8lbs and 9 ounces.

TMZ broke the story in September that Kylie was pregnant with Travis' kid, but she's kept the pregnancy top secret. KJ never confirmed, and totally went underground ... staying out of the spotlight for the last 5 months.

We finally got a shot of her a week ago, but even then she was wearing a baggy black sweatshirt. Now the question -- how long will she keep the new baby under wraps?

Kylie addressed the secrecy in a statement, apologizing for keeping her fans in the dark.

In any event ... mazel tov!

Nicole Eggert told Dr. Oz earlier this month the story of how Scott Baio allegedly got extremely physical with her when she was only 14 and had sex with her at 17 -- something Baio strongly denies -- and we have video from the taping.

As we reported, the episode never aired. Baio's people sent a cease and desist letter to the show, claiming Eggert's timeline didn't make sense. The 'Oz' people shelved the show, although a rep told us they were still investigating.

You hear Nicole claim Baio told her he could help her get ready to have sexual relations with boys her own age. She says she agreed, though it was awkward.

Dr. Oz asks her where the conversation occurred, and she says at her home when her parents weren't there ... presumably, this is when she was 17.

Dr. Oz asked Nicole what he said to lure her into sex, and she said he told her "how much he loved me and, hopefully one day when I was of age, we could be together, and that he understood I needed to go be with boys my own age and it was sort of like a goodbye action.

The show was taped January 10 but, as we said, never aired. Nicole and her lawyer, Lisa Bloom, will appear on Megyn Kelly's show today to tell her story.

Aaron Schwartz -- whose first acting role was playing Dave Karp in "The Mighty Ducks" way back in 1992 -- is stoked the Quack Attack is coming back, and says he wants a piece of the action.

Aaron tells TMZ he's been in contact with some people involved with bringing the 'Ducks' back, and now that it's reportedly green-lit for a TV series reboot ... he's holding out hope he can play a part.

As for who should play the new group of young, misfit hockey players ... Schwartz has a suggestion that shouldn't seem too strange.

Oh and by the way, Aaron is ripped now ... so he could definitely hold his own on the ice.

Cool moment for Shaquille O'Neal -- he got to watch his kid, Shareef, hit the game-winning shot in a big high school hoops tournament ... and Papa Diesel couldn't have been prouder!

Shaq and the entire "Inside the NBA" team were broadcasting live from the CBS Studio Center in L.A. -- where Shareef's Crossroads high school team was participating in the Future of Flight showcase tourney.

The big matchup was Crossroads vs. Beverly Hills High School ... which was tied up at 61 to 61 with seconds left in the game.

Shareef got the last shot -- and made it count ... locking up the victory while Shaq, Barkley and Ernie Johnson went wild!

Of course, Shaq took full credit -- explaining he's been teaching Shareef how to shoot since he came out of the womb!

By the way, after the game Shareef went to the Travis Scott concert, where stars like Terrell Owens were hanging out. Good night for that guy!

STOP THE PRESSES ... a pregnant Kylie Jenner's been spotted out in the real world for the first time since September!!!

TMZ's obtained a shot of Kylie walking with her best friend, Jordyn Woods, and Kris Jenner following closely behind. The trio went to a construction site in Hidden Hills around noon Wednesday.

Check out the video ... it looks like she labors a bit as she gets into her SUV to leave.

As we reported ... Kylie showed her face this week for the first time in months in a Calvin Klein ad with her sisters, but kept her baby bump under wraps.

Sources close to her say she's due soon and, as we reported, baby daddy Travis Scott revealed to friends they're having a girl.

There are 2 ways to see Gregg Sulkin's latest date -- totally awesome or risky business -- 'cause he's getting cozy with Sylvester Stallone's 19-year-old daughter.

Gregg and model Sistine Stallone had a lunch date Wednesday in Bev Hills. Gregg, of course, used to bang Bella Thorne ... before jumping to this girl and that girl. That's all fine and dandy, everyone's got a past, but dude ... this is Sly's little girl.

We know he has some experience with boxing gloves, but he ain't Rocky. We're sure it won't be an issue though.

Tom Taylor -- the young actor who plays Jake in "The Dark Tower" -- got a nice payday for his work in the film, but the big bucks are (hopefully) yet to come ... TMZ has learned.

According to the 16-year-old's contract ... Tom banked $125k for his role in the movie alongside Idris Elba and Matthew McConaughey -- which is nice -- but will make double if he makes it into a sequel ... and $500k if there's a third installment. He'll also haul in $30k per episode if he lands the Jake role in a TV adaptation of Stephen King's story.

Here's the problem -- the movie massively disappointed critics after its summer release and reportedly barely broke even at the box office, taking in $111 million worldwide.

Since then, talk of a sequel's been muted, and even King has expressed concern about a TV project ... saying it would probably need to be a complete reboot.

Guess that's just show business, kid.

Move over, Ball bros -- Shareef O'Neal says the Lakers are his #1 choice when he goes pro ... and if we were Magic Johnson, we'd start working OT to make it happen.

We got Shaq's son touching down in LAX ... and asked who he'd want to draft him since his NBA career is creeping up.

Shareef told TMZ Sports his favorite team and player were the Cavs and LeBron James, respectively ... but there's 1 thing that puts the Purple and Gold above playing with the King.

Kim Kardashian and Kanye West chose a very unique name for baby #3 -- Chicago ... Kanye's hometown ... but it's a good bet she'll be known by a certain nickname.

Kim announced the name on her app by simply posting "Chicago West."

As we reported ... Kim and Kanye had their third child via surrogate, who gave birth Monday to a healthy girl weighing 7 lbs. 6 oz. Kim was in the delivery room during the birth, and we're told she was the first person to have skin-to-skin contact with the baby.

As you know, they already have 4-year-old North, and 2-year-old Saint. We're told the kids have been referring to her by the nickname Chi (pronounced Shy).

Welcome to the family, Chicago!!!