'The Shining' star died on July 11, aged 75, leaving behind her longtime partner, musician Dan Gilroy - who she had been with since 1989 - and he has now applied to a court asking for their relationship to be recognised as a common law marriage.
According to InTouch magazine, Gilroy asked to be appointed the administrator of the estate, which is made up of "cash, real estate, personal effects and household goods of a probable value in excess of $100,000".
He asked to be awarded the majority share of the estate with a portion also going to the actress' three brothers - Shane Duvall, Stewart Duvall and Scott Duvall.
In one of the filings, the publication reports Gilroy stated he is Duvall's surviving spouse "by an informal marriage of 'common law' marriage" and demonstrated an intention to show the couple "had an agreement to be married and demonstrated an intention to create a present, immediate and permanent marital relationship" as well as living together at their home in Texas and representing to others in "that they were married."
The couple didn't have any children together. Duvall was previously married to artist Bernard Sampson between 1970 and 1974.
Gilroy previously paid tribute to his partner following her death, telling The Hollywood Reporter: "My dear, sweet, wonderful life partner and friend left us.
"Too much suffering lately, now she's free. Fly away, beautiful Shelley".
Gilroy previously fronted the Breakfast Club band which featured pop superstar Madonna on drums. The pair dated during their time in the group and the singer credited him with helping her learn how to write music.