The previously secret daughter of mining magnate Michael Wright has failed to persuade Australia’s highest court she deserves more than the $6 million she was eventually awarded from the dead billionaire’s will.

Olivia Mead, then 19, caused a legal sensation in 2015 when she sat in WA’s Supreme Court to announce herself as Mr Wright’s daughter and to challenge the heavily conditioned $3 million payout she had been left by him.

In doing so, Ms Mead put her name to an extraordinary wish-list her lawyers said she might require in her lifetime — which famously included a diamond-studded guitar, a crystal-covered grand piano, a Mexican walking fish, a $2.5 million house, an Audi A4, five pairs of $5000 shoes every year and pilates lessons for the next 75 years.

In a shock judgment, Master Craig Sanderson eventually awarded Ms Mead a record $25 million payout from the massive Wright estate, conservatively estimated at $800 million.

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But that figure was slashed to just over $6 million by WA’s Court of Appeal, who said while the original will did not make adequate provision, the decision to award her $25 million was flawed.

In a final legal foray, Ms Mead’s lawyers argued against that appeal ruling in the High Court in Canberra. But that court knocked them back, ending Ms Mead’s legal avenue to receive more money from her late father’s estate.

During a hearing, Lindsay Ellison said the High Court should look at Ms Mead’s case not just for her sake, but to lay down some ground rules for litigation battles over big estates all over the country.

“One of our complaints about the way the Court of Appeal approached it is they did a particularly mathematical exercise, what is a house worth, what is the right income, what does it add up to and it comes to this unique figure,” Mr Ellison said.

“(The Master) is there to reflect the community ... some might be mean, some might be generous, most of them might be somewhere in between (but) it is not a mathematical exercise.”

But Jane Needham, representing the Wright estate and Ms Mead’s half-sisters Leonie Baldock and Alexandra Burt, said the application was purely about money.

“The complaint, boiled down, is that she did not get enough,” Ms Needham said.

“Clearly the Master was in error when he regarded himself as unfettered and free to determine whatever he wished, despite three days of evidence before him.”

The High Court quorum of Justices Virginia Bell and Patrick Keane agreed, saying there was no ground for Ms Mead and her legal team to appeal.