Prince's sister said the superstar musician had no known will as she filed paperwork asking a court in Minneapolis to appoint a special administrator to oversee his estate.
Tyka Nelson, Prince's only surviving full sibling, said in the court filing that immediate action was necessary to manage Prince's business interests following his death last week.
The size of Prince's fortune is unclear, although he made hundreds of millions of dollars for record companies, concert venues and others during his career, and his estate included about $27m in property.
Ms Nelson asked that Bremer Trust, a corporate trust company, be named administrator of the estate. The court documents say Bremer Bank provided financial services to Prince for many years.
The filing comes less than a week after the pop star died at his home in suburban Minneapolis.
The outpouring of grief and nostalgia prompted fans to buy 2.3 million of his songs in three days.
Prince owned a dozen properties in and around his famous Paisley Park complex in suburban Minneapolis - mostly rural pieces of land and some houses for family members.
Public records show those properties were worth about $27m in 2016.
"He was as big as they get," said Mark Roesler, chief executive of CMG Worldwide, which handles licensing for the estates of Marilyn Monroe, James Dean and other late stars.
He estimated Prince's post-mortem earnings will match top-earning dead celebrities like Elvis Presley, whose estate made $55m in 2015, according to Forbes magazine.
"Will there be a business built up around Prince 60 years from now like James Dean? The answer is unequivocally yes," Mr Roesler said.
If Prince filed a will or created a trust, heirs to his future fortune would be known. But no such documents have yet turned up.
Under Minnesota law, a person can file a will with a probate court in secret. If Prince did so, the fact one exists would become public once a death certificate is filed, but the medical examiner has not yet issued one for Prince.
An autopsy was conducted on Friday and his remains were cremated on Saturday.
L Londell McMillan, a long-time lawyer and former manager of the superstar, declined to comment on Monday about whether the entertainer had a will or any other particulars regarding his estate, but added: "I want to make sure his legacy is respected and protected no matter what role I play."
Mr McMillan was Michael Jackson's lawyer and played a role in his estate, as well as those of rapper Notorious B.I.G. and Sammy Davis Jr.
Several other lawyers who have done work for Prince in the past - including Alan Eidsness, who handled his 2006 divorce from Manuela Testolini Nelson - said they were not handling his estate.
Wealthy people usually create trusts to avoid the public spectacle of probate court, and it is probable Prince did so, according to Irwin Feinberg, a Los Angeles trust and probate lawyer.
Prince was not married and had no known living children.
Ms Nelson is his only full sibling, although he has five half-siblings who could share in his estate if he has no will.