The court filing states that Jackson's parents believe he died without a valid will.
Supporting Katherine Jackson in her petition bid to administer the estate was Jackson's father, Joe Jackson.
The court documents state that Katherine Jackson "intends to marshal assets of the decedent for the exclusive use of the decedent's three children - her grandchildren - after payment of debts and expenses of administration."
The free-spending singer is believed to have $400 million in debt, but his assets - mainly his two song catalogs - are estimated to be worth up to $1 billion, reports CBS News correspondent Ben Tracy.
But Michael Jackson's former wife Debbie Rowe is the biological mother of two of the children: Prince Michael, age 12, and Paris Katherine, age 11. It's not clear whether Rowe wants custody.
"The court has to give preference to the parent, the biological parent; however if that is not in the best interest of the child, the court does not have to follow that," said Charlotte Goldberg of Loyola Law School.
Jackson's youngest son prince Michael II, also known as Blanket, is seven years old. Court records today list his mother as "none."
Jackson friend Al Malnik says the singer wanted him to care for Blanket and the children's longtime nanny says she considers Michael's kids her babies.
His biographer says during his life the megastar purposely kept his family out of the loop.
"So now that Michael is gone, the family finds itself at a great disadvantage because they don't know much about his finances or his personal life," said the biographer, J. Randy Taraborelli.
Earlier, Superior Court Judge Mitchell Beckloff granted Katherine Jackson's request to assume temporary guardianship of her son's children but did not immediately rule on her request to administer their estate.
Beckloff scheduled hearings for July 6 and Aug. 3 to take up the matters, including whether to also approve a request by Jackson to become permanent guardian of her son's children.
So far, a will for Michael Jackson, which might spell out his wishes for care of his children and his estate, has not surfaced. However, TMZ.com reported that Jackson's lawyer has a copy of the singer's will and he intends to file it with the court.
Jackson never told his family who he had in place to handle his business affairs, a person close to the family has told The Associated Press. The person, who requested anonymity because of the delicate nature of the situation, said they were told by the singer's phalanx of advisers that he likely had a will, but it may be many years old.
Jackson's funeral is still in the planning stages, but his father said he would not be buried at Neverland Ranch, the sprawling playground the entertainer built in the rolling hills of Santa Barbara County.
At a news conference outside the family compound, Joe Jackson said the family was carefully considering how best to celebrate the pop star's legacy. He also said the family was waiting until they had a definitive word on the cause of his son's death.
When Jackson died Thursday, he 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 filing lists the children as living at the Jacksons' family compound in Los Angeles' San Fernando Valley.
In her request to take over the children's estate, Jackson's mother listed its value as "unknown."
"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 declaration states that Rowe is the mother of Jackson's two eldest children but lists her whereabouts as "unknown." A family attorney said the Jacksons haven't heard from Rowe since Michael Jackson's death.
An e-mail message sent to Rowe's attorney seeking comment wasn't immediately returned Monday.
The attorney, Marta Almli, wrote in a statement Saturday that "Ms. Rowe's only thoughts at this time have been regarding the devastating loss Michael's family has suffered. Ms. Rowe requests that Michael's family, and particularly the children, be spared such harmful, sensationalist speculation and that they be able to say goodbye to their loved one in peace."
The court filings show that family attorney L. Londell McMillan has joined a team of lawyers to coordinate the family's attempts to take control of Jackson's affairs.
"I don't think there will be anybody who thinks that there is someone better" than Katherine Jackson to have custody, McMillan said Monday on NBC's "Today" show. "She is a very loving host of other grandchildren."
McMillan also said the family was "quite clearly troubled" about the circumstances surrounding Jackson's death, adding he had been healthy enough to be rehearsing for 50 upcoming concerts just days before his death.
Asked whether the family suspected foul play, McMillan said those words were "too strong an indictment."
Edward Chernoff, a lawyer for Michael Jackson's doctor, Dr. Conrad Murray, said in an interview Sunday with The Associated Press that Jackson still had a faint pulse and a warm body when Murray found him in bed and not breathing Thursday afternoon.
Chernoff said Murray was at the pop icon's rented mansion when he discovered Jackson. The doctor immediately began administering CPR, Chernoff said.
"He just happened to find him in his bed, and he wasn't breathing," the lawyer said.
Chernoff said his client never gave or prescribed Jackson the painkillers Demerol or OxyContin, and denied reports suggesting that the doctor gave the pop star drugs that contributed to his death.
Los Angeles County coroner's officials said their autopsy found no indication of trauma or foul play. It also dismissed widely circulated reports that Jackson was riddled with needle wounds, nearly bald, and weighed just 112 pounds when he died, saying that most of that information was totally false.
But because of additional tests, an official cause of death could take weeks to determine. Jackson's family has requested a private autopsy.
Once the investigation is completed, Chernoff said, he expects Murray to be exonerated.