Acoording to The New York Post's Page Six - L'Wren - who took her own life on 17 March - left a simple will leaving her personal effects, including clothing, jewellery, cars and furniture to "Michael Phillip Jagger".
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The paper claims to have seen probate documents which detail that L'Wren owned $1million in "tangible personal property and various other assets".
Also included in her estate is the $8million Manhattan apartment on 11th Avenue where L'Wren was found by her assistant.
The designer's two siblings were not included in the will, which stated: "Except if otherwise provided in this will, I have intentionally omitted to provide herein for any other of my heirs living at the date of my death."
L'Wren was born Luann Bambrough, and raised by her adoptive Mormon family in a small town in Utah. She left home, aged 17, to peruse a modeling career and changed her name as she began her new life in New York.
She was reportedly estranged from her sister Jan, who was not included in the will. Neither was her brother Randy.
Randy was the only Bambrough family member to be present at L'Wren's funeral, which took place this week in LA.
The intimate memorial took place at the Hollywood Forever Funeral Home and Cemetery, and security patrolled the area to ensure L’Wren’s family and friends’ privacy.
Among the reportedly 70 friends and family attending the ceremony were close friends of Ms Scott from the fashion industry and her company, including her long-time assistant, Brittany Penebre.
L’Wren’s long-term partner Mick was accompanied to the funeral by his children and his grand-daughter Amba Jackson, Jade’s daughter.