The document leaves assets estimated at $710,000 to Smith's now-deceased son, Daniel, and also gives Stern custody of Daniel, who was a minor in 2001, when the will was written.
In a probate petition signed May 7 by Stern, he asked a judge to recognize the document as Smith's last will and him as its main executor. The petition also names Smith's 8-month-old daughter, Dannielynn, as her survivor, and Larry Birkhead as the infant's father.
• Get the developments on the tragedy in FOXNews.com's Anna Nicole Smith Celebrity Center.
Daniel was 20 when he died in September in the Bahamas from a lethal combination of drugs, days after Smith gave birth to Dannielynn. The girl was briefly thought to be fathered by Stern before paternity tests showed the father was Birkhead.
The probate proceeding to sort out Smith's assets, debts and taxes will lead to the establishment of a trust with Dannielynn as its sole beneficiary, said Stern's attorney Bruce S. Ross.
With the trust, the girl could inherit the estate of Smith's late husband, Texas oil tycoon J. Howard Marshall II, estimated to be worth $500 million.
Birkhead also filed papers Monday to ask a judge to appoint him as guardian of Dannielynn's estate.
"As the child's father and caregiver, (Birkhead) is in the best position to protect and safeguard the interests of his child as guardian of her estate, including her interests in the estate of her deceased mother," the petition said.
A June 19 hearing was scheduled to hear both petitions.
Smith was 39 when she died Feb. 8 in Florida from a mix of prescription drugs.
Get the developments on the tragedy in FOXNews.com's Anna Nicole Smith Celebrity Center.