Jude Law -- I Support ALL My Kids -- Especially The Illegitimate One

Jude Law is on the hook for more than a quarter million dollars a year in child support ... and the biggest share goes to his illegitimate daughter -- NOT the kids he had with his ex-wife, Sadie Frost.

We got the agreement between Law and his baby mama, Samantha Burke ... with whom he had a brief fling in 2008. The doc shows Law agreed to make child support payments for their daughter, Sophia, based on his income -- $3.4 mil in 2009 and $2.4 mil in 2010.

According to the legal docs, Law pays more than $13K in monthly support to Frost -- around $4,500 for each of their 3 kids.

But ... the daughter he had with Burke gets more than double that amount -- $9K a month -- and it goes up every few years until she's 18.