Media mogul Rupert Murdoch is all smiles as he enters court with his heir apparent Lachlan on second day of battle over News Corp empire

Rupert Murdoch smiled and looked confident on the way into the second day of the legal battle over the future of his estate.

The media tycoon, 93, gave a grin as he walked into the court in Reno, Nevada, with his son, Lachlan, 53, who is his chosen successor.

Murdoch's other three eldest children looked stony faced as they arrived but Elisabeth, 55, managed a brief smile.

She and her siblings Prudence, 65, and James, 51, are facing off against Lachlan and their father for control of his media empire in the case, which is being held in private.

The parties were in court for a grueling 11 hours on Monday, and the hearing has been extended from five days to seven, meaning it ends next Tuesday.

The extra time was likely due to the complexities of the dispute, which concerns the $15 billion in assets owned by the Murdoch family estate.

The state controls Murdoch's empire including US TV network Fox News and News Corp, which is the parent company of the Times, Sun, New York Post, and Wall Street Journal newspapers.

Under the terms of the controlling trust, which were agreed in 1999 when Murdoch divorced his second wife Anna, his four eldest children will each have one vote to decide matters related to his empire after he dies.

Murdoch currently has the controlling vote and cannot be outvoted.

Murdoch is seeking to amend the terms so Lachlan will have control, as his father does now, instead of equal distribution with his siblings.

He is said to be worried the three other siblings would push Fox News in a more liberal direction, to the claimed detriment of the business. 

The power grab has already been described as the kind of move that seems like a storyline out of Succession, which was loosely based on the Murdoch dynasty. 

Lachlan has been chairman and chief executive of the Fox Corporation, which is what remained of the company after Murdoch sold the 21st Century Fox film and TV studio to Disney for $71 billion in 2019.

Murdoch arrived at court on Tuesday in a convoy of three SUVs and walked gingerly up the steps to a side entrance of the court.

Lachlan went ahead of his father and tried to open a door, which wouldn't open.

He eventually found the right door and held out his hand to allow Murdoch to pass ahead of him.

Prudence, Elisabeth and James arrived in a convoy of five SUVs and walked up through the same entrance.

Nobody responded to requests for comment.

On Monday, the first day of the hearing, Murdoch skipped out at lunchtime while the children stuck it out until 7pm for a grueling, 11-hour day.

Though no documents in the case were made public, the docket for the case showed more than 500 have been filed since October and nearly 80 lawyers were working on the case.

Also attending court was former Attorney General Bill Barr, who is working with Murdoch to rewrite the trust.

The dispute is already causing a recalculation at Fox News, and CNN reported that the network's hosts were discussing how to win favor with James, should he take it over.

The US TV network's media correspondent Brian Stelter reported: 'Prominent Fox hosts talked openly about how they might reposition their own personal brands in the event of a James-led takeover.

'Some Fox personalities even tried to establish back-channel relationships with James, even though Lachlan was the boss.'

The case is happening in Reno due to its favorable probate laws that guarantee privacy.

In Murdoch's case, that means the documents that have been filed since last October are under seal, and therefore not public.

Probate commissioner Edmund Gorman said the interests of the public did not outweigh the fact the case was a private matter.

Only after a torrent of media inquiries did the court even put any information up on its website, and even then the parties were referred to as 'Doe' rather than by their names.

There is no mention of Murdoch by name, instead the matter is listed as 'PR23-00813 - **SEALED** TRUST: THE DOE 1 TRUST'

Several US media outlets including CNN and the New York Times did try to gain access to the hearings, but their application was rejected by a judge.

A local nonprofit, Our Nevada Judges, which advocates for greater access to Nevada courts, also joined in the efforts.

'The public have a right to know what's happening inside the court,' its founder Alex Falconi said.

'This case involved Rupert Murdoch and News Corp. It's obviously worthy of public scrutiny.'

The only concession by the court was that the names of lawyers and other non-parties were made public.