NBA Star Elton Brand -- College Sweetheart Files for Separation

Elton Brand is now a free agent ... professionally and personally -- the NBA superstar's wife has filed for separation.

Brand's now estranged wife Shahara Simmons filed the docs a couple weeks ago ... shortly after their 9th anniversary. They met during college at Duke University and have 2 children.

In Sahara's docs she says they hashed out separation of assets back in April, and all that's left to hammer out is child custody and child support.