Lawyers for Mrs Rinehart's company, Hancock Prospecting, and the heirs of mining pioneer Peter Wright and engineer Don Rhodes, returned to court in Perth on Thursday.
They wrangled over the implementation of a judgment that found Wright Prospecting and DFD Rhodes were owed some of the spoils from the massive Rio Tinto-operated Hope Downs mining complex, in WA's ore-rich Pilbara region.
These included who should calculate the royalty amounts, the interest rates that could be applied to the vast sum, potential damages for Hancock Prospecting's breach of contract, future revenue payments and what documents Hancock Prospecting would be required to supply.
Justice Jennifer Smith indicated that Hancock Prospecting should give Wright Prospecting and DFD Rhodes decades of royalty accounts as a first step in determining the monetary settlement, as she detailed the orders she would likely make at a future date.
The years-long complex legal case, which pitted Hancock Prospecting against Wright Prospecting and DFD Rhodes amid allegations of decades-old contract breaches, ended last week with Justice Smith handing down a 1655-page judgment.
Justice Smith dismissed Wright Prospecting's claim for a half share of some of Hancock's iron ore deposits, worth billions of dollars, leaving Mrs Rinehart in control of the prized assets.
Rio Tinto was also involved in the battle as the joint-venture partner in Hope Downs.
The 51-day Western Australian Supreme Court trial featured sensational allegations against Mrs Rinehart, which she vehemently denied.
These include that the billionaire devised an unlawful scheme to defraud her children and allegedly tried to have her father Lang Hancock's wife, Rose Porteous, deported in the 1980s amid fears she would inherit shares in Hancock Prospecting.
Mrs Rinehart inherited her father's iron ore discovery in the Pilbara region and forged a mining empire after he died in 1992.
She developed mines from tenements at Hope Downs, signing a deal in 2005 with Rio Tinto which has a 50 per cent stake in the project.
The Hope Downs mining complex near Newman is one of Australia's largest and most successful iron ore projects, with multiple open-pit mines.
Mrs Rinehart's wealth is estimated to be about $40 billion.
The parties will return to court on May 1 to continue the hearing.
