Gina Rinehart's estranged children are seeking to take fresh legal action against their mother for the alleged underpayment of mining royalties while she was trustee of the family's $5 billion trust.

In the NSW Supreme Court on Tuesday, John Hancock and Bianca Rinehart sought preliminary discovery of documents to ascertain whether or not to proceed with legal action against their mother.

The royalties are paid by multinational mining giant Rio Tinto to Mrs Rinehart's flagship company Hancock Prospecting under agreements signed by the late Lang Hancock over several Pilbara mines in the 1960s.

The children say a share of that income should be distributed to them and their younger half-siblings Hope and Ginia via the trust, of which they are beneficiaries.

Ms Rinehart and Mr Hancock's barrister, Christopher Withers, told Justice Richard White there was no way to ascertain from the company's annual reports how much was paid by Rio Tinto to Hancock Prospecting and how much of that translated into dividend payments to the family trust.

He said it is likely certain mines have been excluded or the methodology used to calculate the royalties was incorrect.

"We need to know the full picture to know whether there has been an underpayment," Mr Withers said.

Mrs Rinehart, 61, Australia's richest person, is resisting preliminary discovery.

Justice Richard White said there had to be a sufficient indication that there might be a claim before he would order discovery.

Mr Hancock and Ms Rinehart may sue their mother for breaching her duties as trustee, a position she held from 1992 until October 2013, when she stepped down amid a bitter court case.

Last month the NSW Supreme Court appointed Ms Hancock, 38, as replacement trustee.

Mr Withers said the plaintiff children could also use the documents to pursue Hancock Prospecting for knowing involvement in the breach.

Mrs Rinehart's barrister Bruce McClintock said his client had previously offered to hand over documents detailing the payments, subject to conditions including confidentiality provisions.

"If they saw the documents and examined them they would see they would have no case," he said.

"We are perfectly prepared to offer the documents on the same basis now."

Mr McClintock also said it was "wrong" to assume Mrs Rinehart would benefit from any underpayment to the trust or the beneficiaries.

Referring to the long history of bitter litigation between the family members, he said: "There seems to be an assumption that my client would be prepared to cut off her nose to spite her face. That is not the case."

Ms Rinehart and Mr Hancock are also fighting their mother in separate Federal Court proceedings.

In that case, they claim Hancock Prospecting's most valuable assets, including the Hope Downs mine, belongs to another family trust rather than to the company.