Jesse Williams isn't looking for a fight over child custody in his divorce ... according to docs.
TMZ obtained the divorce petition filed by the "Grey's Anatomy" star on April 11, and he is requesting joint physical and legal custody of their 3-year-old and 1-year-old kids.
Jesse and Aryn Drakelee-Williams got married in 2012. The docs do not list a date of separation.
As for spousal support -- Jesse checked the box asking the court to deny her spousal support, they are working it out in mediation instead. That sometimes means the couple has a prenup ... but we're told that's not the case for Jesse and Aryn.