The guardianship papers were filed in Los Angeles Superior Court on Monday. A hearing has been set for Aug 3.
Jackson left behind three children: Michael Joseph Jackson Jr., known as Prince Michael, 12; Paris Michael Katherine Jackson, 11; and Prince Michael II, 7. The youngest son was born to a surrogate mother.
The filings show that Katherine Jackson is also petitioning to take over the children's estate. Its value is listed as "unknown" in the filing.
The filing lists the children as living at the Jacksons' family compound in the San Fernando Valley, northwest of Los Angeles.
"Minor children are currently residing with paternal grandmother," the filing states in an explanation of why Katherine Jackson should be appointed guardian. "They have a long established relationship with paternal grandmother and are comfortable in her care."
The filings provide no other declarations by Katherine Jackson, nor do they state whether Michael Jackson left a will.
The filings note that Deborah Rowe is the mother of the Jackson's two eldest children, but list her whereabouts as "unknown."
For Michael Jackson's third child, known as Blanket, the filing states "None" for the mother.
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