Gina Rinehart will take the battle with her children over mining royalties behind closed doors after the High Court agreed on Wednesday that it should not be heard "in the public spotlight".

Mrs Rinehart’s two eldest children – John and Bianca – wanted a judge to hear the dispute over a series of deeds signed from 2003-2010 that reduced their interest in three Hancock mines in the Pilbara from 49 to 24 per cent.