Moon Zappa Divorce Our Kid Will Still Get the Star Treatment

4/11/2014 12:20 AM PDT

Moon Zappa and "Matchbox Twenty" drummer Paul Doucette just finalized their divorce ...  and they agree on one thing ... their daughter will live like a glamorous Hollywood princess.

According to their divorce docs ... 9-year-old Mathilda will get the standard celeb kid trappings -- private schools and music lessons -- but Moon and Paul also signed off on ... "photo or video shoots for Mathilda's career." 

Also ... they've agreed to never allow her to be "baby-sat by a hotel baby-sitting service, fun rooms or the equivalent."

The docs show Doucette will pay Zappa $8K a month in spousal support for the next 5 years ... and another $6K a month in child support. 

Plus, they'll split the money Paul made from more than 50 songs he's written or co-written -- including "Matchbox Twenty" gems ... "If You're Gone" and "How Far We've Come." 

Sappy adult contemporary -- supporting famous kids since 2014.