John Hancock and Bianca Rinehart are seeking an account of profits from the mining magnate's major iron ore projects, including Roy Hill, Hope Downs and Mulga Downs, arguing their mother bolstered her own shareholding at their expense.

The explosive new claims were made public after a Federal Court judge refused Mrs Rinehart's urgent application to suppress the case.

Mrs Rinehart and her flagship mining company, Hancock Prospecting, claimed Mr Hancock and Bianca Rinehart had launched legal action for the "collateral purpose of obtaining publicity for the allegations as a tactic to put pressure" on them.

But on Wednesday Justice Peter Jacobson revoked the interim suppression order he made earlier this month, saying the applicants failed to make good the submission that the plaintiff children's proceeding is an abuse of process.

As soon as the order was lifted, a detailed statement of claim was publicly released.

Mrs Rinehart immediately fired back with a statement painting her two eldest children, by her first husband Greg Hayward, as spoiled brats.

"I feel parents everywhere cringe at this scene, watching extremely privileged children suing to get even more money unearned by them, after their mother's lifetime of hard work," Mrs Rinehart said via her spokesman, Jason Morrison.

Mr Hancock responded almost immediately, saying:  "Rational minds will see through this latest load of propaganda. The judge today found no credible basis for the allegations of my mother's lawyers - and after her loss, a repeat of them by her PR agent."

Mr Hancock and Bianca Rinehart's case could  significantly reduce the   wealth controlled by Australia's richest person.

They claim their late grandfather, Lang Hancock, had intended the family trust hold 49per cent of the shares in Hancock Prospecting on behalf of his grandchildren.  They say as trustee, Mrs Rinehart significantly reduced the beneficiaries' number of shares while beefing up her own stake in the company.

Central to the case is the allegation Mrs Hancock transferred mining interests out of the trust – now worth an estimated $5billion – and into her flagship company Hancock Prospecting.

Mr Hancock and Bianca Rinehart have asked the court to declare that Mrs Rinehart committed a "fraud on the power" in asking her children to enter into a series of deeds in the mid-2000s, that were designed to settle the family's various disputes over money and entitlements in private.

Justice Jacobson's refusal to continue the suppression order means the latest iteration in the family's long and bitter dispute will be played out in the public eye.

Mrs Rinehart and Hancock Prospecting had argued there was "a real risk of commercial harm" if the allegations were made public because potential lenders and investors might decline to deal with the Hancock Prospecting companies.

But Mr Hancock and Bianca Rinehart, supported by Fairfax Media (publisher of the this website), News Corp and Nine Network, argued against the suppression order.

Justice Jacobson said the allegations must, by law, be disclosed to Hancock Prospecting's counterparts, undermining the "commercial inconvenience" argument. Further, the public interest in open justice and the entitlement of the media, including those who formally opposed the suppression order, must be taken into account, Justice Jacobson said.