Tiger Lily Hutchence Geldof had a low-key celebration for her 18th birthday on July 22.
But despite coming of age, there was no sign of much inheritance from her late father, INXS frontman Michael Hutchence.
Her Australian family told New Idea the rocker would have been upset to leave his daughter nothing.
"He would have hated this outcome to his will," the singer's brother, Rhett Hutchence, said.
"Michael worked very hard for what he achieved.
"He wanted his family to have his hard-earned wealth."
Rhett, 52, said the whole family were puzzled as to what happened to the rocker's supposed vast fortune.
It was widely believed the musician was worth an estimated $30 million at the time of his death.
He died in 1997 after hanging himself in a Sydney hotel room.
As well as royalties from his music, Hutchence was believed to own extensive properties in Australia, as well as France, England and Indonesia, according to the Daily Mail.
However his only child Tiger Lily, who was adopted by Bob Geldof following the deaths of both her parents, is entitled to next to none of his estate.
The barrister who drew up the rocker's original will, Andrew Young, said in a 1998 affidavit: "He told me that his principal concern was his daughter, Tiger Lily, and that he had 'structured his financial affairs' to help her."
He had also bequeathed half a million dollars to the charities, Amnesty International and Greenpeace.
But not long before his death he told his mother, "there's virtually no money left", while they were on a holiday in Vienna.
"The will was black and white," said Rhett.
"Michael thought he had control of his assets but in the end, it only worked with Michael still alive.
"On his death he owned little or nothing."
The executor's report, made public in 2005, showed that Hutchence had $506 in cash and $572 in a shared band bank account at the time of his death.
To further shock the family the properties Hutchence claimed to own weren't, in fact, his to bequeath, and his music royalties were also excluded from his estate.
Tiger Lily, whose full name is Heavenly Hiraani Tiger Lily, won't be left penniless though.
She has been raised by Geldof since the death of her mother Paula Yates in 2000 of an accidental heroin overdose.
The Mail reports Tiger Lily also received a decent payment from a television series based on her father.
Tiger Lily was just one year old when her father died, and four when she became an orphan following her mother's death.
Her latest bereavement was the death of her half sister Peaches Geldof earlier this year, who died of a heroin overdose like Paula Yates.