JOHNNY DEPP and ex, VANESSA PARADIS are battling over their wild-child daughter Lily-Rose – who’s 13 going on 30!

The “Pirates of the Caribbean” star, 49, wants to prevent the precocious teen from pursuing a Hollywood ca­reer, sources say, but singer/actress Vanessa, 39, doesn’t agree.

“Johnny still thinks of Lily-Rose as the little 7-year-old that he almost lost to E. coli poisoning, and he’s deeply concerned that Vanessa is letting her run wild,” said an insider.

“He doesn’t want Lily-Rose, or her brother Jack, thinking about anything but school until they’re 18. But Van­essa is letting Lily-Rose explore her creative side by allowing her to wear funky outfits, and she’s schlepping her to acting auditions.

“Vanessa and Johnny have been having screaming matches over Lily-Rose. It’s gotten ugly.”

Depp and Vanessa hooked up in 1998, but never married, and raised Lily-Rose and Jack, 10, at their home in the South of France. Since their split, the actor has been living in Los Angeles while Vanessa is looking for a home in Malibu.

As The ENQUIRER has reported, the French beauty is waging a full-scale palimony battle for her share of Depp’s $350 million fortune, and she’s banned one of his latest girlfriends, bisexual actress Amber Heard, from going near their children.

Depp is also dealing with the ongoing medical problems of his 77-year-old mother, who recently moved from Kentucky to Los Angeles for specialized care.

“Johnny enlisted his mom to help out with parenting duties, but her health issues are taking precedence now,” said the source.

“He’s so worried about Lily-Rose that he’s even turned to his good pals Brad Pitt and Angelina Jolie for advice.

“Johnny knows that if his little girl gets involved in the Hollywood scene, she’s going to grow up a lot faster. And he doesn’t want to see her turn into the next Lindsay Lohan.”