Gina Rinehart has lost control of a A$5 billion family trust that holds 24 per cent of Hancock Prospecting after a court appointed her eldest daughter Bianca Rinehart trustee.

NSW Supreme Court appointed her daughter trustee of the Hope Margaret Hancock Trust, which holds 23.4 per cent of the family's flagship mining company on behalf of Rinehart's four children.

But the court dismissed other claims that changes to the constitution of Hancock Propsecting had been inappropriately decided to by Rinehart.

The falling iron ore price has degraded Rinehart's wealth it is estimated she has lost some A$5.99b over the past year but she maintains her position as Australia's richest person with A$14.02 billion.

Rinehart, who voluntarily relinquished the role of trustee, in October 2013 before hearings, has been ordered to deliver up the trust documents and account to the new trustee. Rinehart's own legal advisors are contesting and fighting to have the Federal Court proceedings dismissed or alternatively permanently stayed.