The case has been unfolding behind closed doors in state court in Reno, with most documents under seal.
But reporting by The New York Times, which said it obtained some of the documents, revealed Murdoch's efforts to keep just one of his sons, Lachlan, in charge and ensure that Fox News maintains its conservative editorial slant.
Media outlets including the Times and The Associated Press are asking the Nevada Supreme Court to unseal the case and make future hearings public.
The court is scheduled to hear arguments in the afternoon in Carson City, the capital.
Murdoch's media empire, which also includes The Wall Street Journal and New York Post, spans continents and helped to shape modern American politics.
Lachlan Murdoch has been the head of Fox News and News Corp since his father stepped down in 2023.
The issue at the centre of the case is Rupert Murdoch's family trust, which after his death would divide control of the company equally among four of his children - Lachlan, Prudence, Elisabeth and James.
Irrevocable trusts are typically used to limit estate taxes, among other reasons, and can't be changed without permission from the beneficiaries or via a court order.
Rupert Murdoch has attempted to alter the trust, however, and Prudence, Elisabeth and James have united to try to stop that.
James and Elisabeth are both known to have less conservative political views than their father or brother, potentially complicating the media mogul's desire to keep Fox News's political tone.
The dispute has had many twists and turns, including a probate commissioner ruling against Rupert Murdoch in December.
In a 96-page opinion, the commissioner characterised the plan to change the trust as a "carefully crafted charade" to "permanently cement Lachlan Murdoch's executive roles" inside the empire "regardless of the impacts such control would have over the companies or the beneficiaries" of the family trust, according to the Times.
Adam Streisand, a lawyer for Rupert Murdoch, told the newspaper at the time that they were disappointed with the ruling and intended to appeal.
Another evidentiary hearing is scheduled for May.
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