Mining magnate Gina Rinehart has been ordered to pay the legal bills of three of her four children incurred in their long-running battle to remove her as trustee of the family's multibillion-dollar trust.

Mrs Rinehart, who is Australia's richest person and the wealthiest woman in the world, has also been ordered to pay costs to media organisations Fairfax Media (publisher of smh.com.au and The Australian Financial Review), Nationwide News (publisher of The Daily Telegraph and The Australian) and the Australian Broadcasting Corporation.

The mining magnate has been fighting her three eldest children - John Hancock, Bianca Rinehart and Hope Welker - in the courts over control of the trust since September last year.

In the NSW Court of Appeal today, Mrs Rinehart and her youngest daughter and ally, Ginia Rinehart, were ordered to pay the plaintiff children costs they incurred in opposing her attempts to stay earlier court decisions.

Mrs Rinehart had asked the court to stay a decision made on December 19, 2011, which allowed the media to publish details of the family feud that had been suppressed by another judge in October.