Sara Gilbert and Linda Perry Legal Separation Finalized

Sara Gilbert and Linda Perry's split is finally official -- because a court has signed off on everything ... including what happens with their kid.

According to legal docs, obtained by TMZ, the former couple's legal separation became official last week, and it looks like a pretty clean break ... with the couple agreeing on a 50/50 split on custody.

As you know, Sara and Linda have a 6-year-old son together, Rhodes, and they will have joint physical and legal custody ... so, both will continue to weigh in on various decisions, such as school and medical issues.

Day-to-day decisions over the boy's well-being will be the responsibility of the parent he's with at any given time. Neither of them will pay child support to the other -- they're both very successful, after all.

When it comes to how they're going to be splitting up their property and other assets ... there's a separate agreement, but those details aren't public.

Sara and Linda got hitched in 2014, with SG giving birth to Rhodes in 2015. She's got 2 other children from previous relationships. Sara created and co-hosted "The Talk" for years, and has since gone on to star in the "Roseanne" spinoff, "The Conners."