Anderson .Paak's divorce is starting to pick up movement ... with his estranged wife requesting primary physical custody of their 2 kids -- and spousal support.

The musician's estranged wife Jae Lin filed legal docs in L.A., obtained by TMZ, earlier this week ... Jae says she wants to share legal custody of their children, ages 9 and 13 ... but she wants primary physical custody, with Anderson getting secondary physical custody and visitation.

She's also requesting spousal support, and wants to terminate the court's ability to award such support to Anderson.

She checked the box for "irreconcilable differences" as the reason their marriage needs to end. The pair tied the knot in November 2010, just weeks before welcoming their eldest child. She wrote "TBD" in the court docs for their separation date ... which Anderson also did when he filed in 2024.

Notably, neither Anderson nor Jae seemed worried about moving forward with their divorce quickly as it sat still in the court system ... though the new movement comes as the "Leave the Door Open" hitmaker is rumored to be dating Jeannie Mai.

We caught her heading into Anderson's jazz speakeasy restaurant and bar, Andy’s in Hollywood, 2 weeks ago ... and she stayed mum about their rumored romance -- though we did see them appear to be getting close inside.

This sighting came just weeks after they were seen cuddled up at Andy's looking very much like a couple. Whatever they have going on, they're clearly trying to keep on the DL!