Sydney - Australia's richest person Gina Rinehart on Tuesday said she plans to relinquish control of a multi-billion dollar family trust, ending a long-running and bitter feud with two of her children.

The mining mogul's lawyers told a Supreme Court directions hearing in Sydney that her decision meant the two-year dispute was "effectively over", the Sydney Morning Herald reported.

Two of Rinehart's four children - John Hancock and Bianca Rinehart - have been embroiled in a court case to have her removed as head of the trust which was established by their grandfather, the late Lang Hancock.

They allege their mother acted "deceitfully" and with "gross dishonesty".

Rinehart denied the accusations.

The protracted row stems from a family trust set up by Hancock in 1988 with his four grandchildren as the beneficiaries.

His daughter Gina Rinehart was to run the trust, which holds a 23.4 per cent slice of her iron ore company Hancock Prospecting, until the youngest grandchild turned 25 in 2011.

But just days before this date she allegedly sought to delay the payout until 2068, saying it would avoid a huge capital gains tax bill and prompting Hancock and sisters Bianca Rinehart and Hope Rinehart Welker to take court action.

Hope Welker later pulled out, but not before documents submitted to the court exposed the bitter battle within the family headed by Gina, whose fortune was estimated earlier this year by Forbes at US$17 billion (S$21 billion).

Bruce McClintock, a lawyer for Gina Rinehart, said the court proceedings had placed huge pressure on his client and created "untenable risk" of damage to Hancock Prospecting.

"The increased demands on her time in dealing with the... plaintiff's issues has taken valuable time away from her responsibilities," he said, according to the Herald.

Reports said her decision sets up a showdown for the position of trustee between her four children, who also include Ginia, the only child to side with her mother and who spoke out against her brother and sisters, saying: "This case is motivated entirely by greed."