Lawyers for Australian mining magnate Gina Rinehart, one of the world's wealthiest people, told her estranged children on Friday to "go out and earn for themselves" after she lost a legal challenge to keep details of a family dispute out of the media.

Rinehart, identified by Forbes magazine the world's 29th richest person with a fortune of $18 billion, has been battling her three oldest children who want her ousted as trustee of the multi-billion-dollar family trust.

The children want to be appointed trustees in her place and they have made allegations of "serious misconduct" which Rinehart disputes.

Friday's High Court decision is likely to result in litigation details being made available to the media for reporting.

"The plaintiff's children have seen fit not to follow sound advice from family friends that if they are not happy they should go out and earn for themselves," Rinehart's law firm Corrs Chambers Westgarth said in a statement.

Lawyers for the three children, Hope Rinehart Welker, Bianca Rinehart and John Hancock, and media interests argued that the dispute was of a family matter, not commercial, and therefore it could be made public.

In one key issue under dispute, Rinehart is arguing that pre-nuptial requirements applied to her children were in accordance with terms of a confidential deed that could provide giant pay-outs for them from the family's growing iron ore business.

However, income from the trust after tax was too small to pay for luxury homes, so homes were provided to the three eldest children in addition to trust dividends and other benefits, according to Rinehart's lawyers.

Rinehart's youngest daughter, Ginia, who has supported her in the dispute, said in a statement released to media the case was "motivated by greed, and I have no doubt that one day soon my brother and sisters will regret putting money before family".

Rinehart is the daughter of Lang Hancock, an Australian prospector credited with discovering giant deposits of iron ore in the 1950s that now make up Australia's largest export base.

The 58-year-old widow is also building stakes in some of Australia's largest media companies, drawing comparisons to another famously powerful Australian, Rupert Murdoch, head of News Corp and now a U.S. citizen.