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"After much thought and careful consideration, we have made the difficult decision to divorce," the couple said in a statement. "We go forward with love and friendship for one another and a commitment to co-parenting our children whose privacy we ask to be respected during this difficult time."
Affleck, 42, and Garner, 42, have three children: Violet, 9, Seraphina, 6, and Samuel, 3.
In 2014, Garner told InStyle magazine of their parenting dynamic: "I know who wants what lunch, and I've done all the school paperwork and filled out the emergency cards. Ben doesn't know that stuff exists. He is in charge of laughter. No matter how much I tickle them or toss them or chase them around, it's not the same. If I'm the slow, steady drumbeat, he's the jazz."
"Although they will file for divorce, it won't be done immediately," reports TMZ. "They are working things out with a mediator and business managers. The divorce will be filed when all of the property and custody issues are resolved."
According to one report, the celebrity power couple is headed for a $150 million divorce.
The couple, whose anniversary was Monday, announced their divorce on Tuesday -- but there may be a reason behind the timing.
"Waiting until after their 10th wedding anniversary might make sense from a Social Security perspective," notes MarketWatch. "Divorcing before 10 years of marriage would forfeit any spousal benefits they might choose to claim in the future."
Affleck and Garner got married in 2005 after meeting on the set of "Daredevil." Next year, Affleck will play Batman in the highly anticipated "Batman v Superman: Dawn of Justice."