NAS & KELIS ARE OFFICIALLY DIVORCED! HE HAS TO PAY HER $10,000 A MONTH IN CHILD & SPOUSAL SUPPORT!

After an eternity of legal war, the marriage between rapper Nas and singer Kelis is officially kaput.

TMZ obtained legal docs, filed last Friday in L.A. County Superior Court, which show that the marriage has been terminated -- but there are still a few more nasty battles to fight ... like child custody and spousal support.

Currently, Nas is ordered to fork over roughly 10k a month for child and spousal support -- which he claims he can't afford.

So, the next round should be all sorts of fun.

Stay tuned.