The wealthy heirs of mining pioneer Peter Wright and engineer Don Rhodes in April won some of their claims for spoils from the massive Hope Downs mining complex, in WA's ore-rich Pilbara region.
Hancock Prospecting, of which Mrs Rinehart is executive chair, is fighting parts of a complex court ruling, lodging appeals last week against some of the court orders related to the decision, including findings related to decades-old partnership contracts between her company and Wright Prospecting and DFD Rhodes.
On Tuesday, more than two dozen lawyers for the parties returned to the WA Supreme Court in Perth to make submissions about the hefty legal bill resulting from the ongoing 16-year-long stoush, which some commentators have suggested could run beyond $100 million.
Wright says Hancock should pay most of its costs because of "favourable outcome" on many of its claims.
"The overall point we make is that the HPPL parties ought to pay 75 per cent of our costs," Julie Taylor SC told Justice Jennifer Smith.
Hancock wants the same from Wright, prompting Justice Smith to observe that it would equate to each paying half.
Mrs Rinehart's children, John Hancock and Bianca Rinehart, who were joined to the case over a previous claim stating their grandfather left them a hefty share in the Pilbara mining resources he discovered in the 1950s, should pay some of Wright's and their own costs because their case failed, Ms Taylor said.
Rhodes should pay Wright Prospecting's costs relating to their legal conflict because their claims were also unsuccessful.
Also at issue is how the costs should be calculated, with Justice Smith suggesting an experienced referee could oversee it.
Rio Tinto was also involved in the battle as the joint-venture partner in Hope Downs.
Mrs Rinehart inherited her father Lang Hancock'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.
The hearing continues.
