Analysis: Inheritance row behind parting of the ways at Murdoch's News Corp

But it seems that the two young daughters, Grace and Chloe, he had with Ms Deng, have caused a rift with his other children, and contributed to the sudden departure from the News Corporation global media empire last week of his eldest son, Lachlan.

According to various people close to the family, one of the reasons behind the resignation of Lachlan Murdoch - the deputy chief operating officer of News Corporation and widely seen as his father's heir apparent - was a bitter disagreement about the future ownership of the company.

The 30 per cent stake - worth $6bn - that Murdoch Snr holds in News Corporation will pass to his three children by his second wife, Anna, who he was married to for 31 years. They are Lachlan, Elisabeth and James. Prudence, a daughter from his first marriage, also benefits from the arrangement, which allows these four children each to appoint a director to the board after their father dies.

Ms Deng and Mr Murdoch are understood to want to change that, allowing Grace, three, and Chloe, two, to eventually share control of the company, whose assets span from newspapers to satellite television to movie studios.

The Times, The Sun and BSkyB in the UK, the Fox television network and the satellite business DirecTV in the US, are among the prize assets the international media conglomerate which Mr Murdoch has built up over the past 50 years from a single Australian newspaper.

Over the weekend, Mr Murdoch attempted to end speculation that a damaging split has occurred in his family. "There is no dispute. All my children will be treated equally," he said. Following on from his statement on Friday that he was "particularly saddened" by Lachlan's departure, the elder Murdoch added that he looked "forward to the day when Lachlan wants to return to our company".

That is unlikely to happen soon. Several reports over the weekend said that the backdrop to Lachlan's announcement that he was returning to Australia with Sarah O'Hare, his model wife, and their baby son, Kalan, were months of disagreement with his father, not only about inheritance rights but also about the imperious way Mr Murdoch runs the company.

In trying to create a family dynasty, in which one of his children would replace him, Mr Murdoch has created a hothouse, giving senior roles to his adult offspring and then expecting them to prove themselves and to compete with each other. Mr Murdoch's former wife, Anna, said in an interview in 2001 that she hoped none of her three children would succeed their father. "There's been such a lot of pressure that they needn't have had at their age," she said shortly after her marriage ended. She added that she thought there would be "a lot of heartbreak and hardship" over succession.

Elisabeth Murdoch, 36, has trod a path similar to her brother Lachlan. Having been director of programming at BSkyB in the UK, she quit in 2000 - shortly after her father married Ms Deng - to set up her own television production company in London. In an interview last year, she said: "Sometimes it's easier to be a Murdoch outside News [Corporation] than inside."

The most pressure was piled on Lachlan, Mr Murdoch's first-born son, who went directly to his father's company in 1994 after graduating from Princeton University. His was sent to the Mirror, a newspaper in Sydney, where he started out as an intern cleaning the printing presses, before rising rapidly through the company and moving to New York in 2000 to become deputy chief operating officer of the entire group.

While Mr Murdoch has suggested Lachlan and his second son, James, might ultimately share control of the company - possibly splitting it between newspapers and broadcasting assets - he has also described Lachlan as the "first among equals".

Mr Murdoch faced down charges of blatant nepotism when he moved James from his role running Star TV in Asia to the powerful position of chief executive of BSkyB in the UK in 2003 - a crucial point in the broadcaster's history. News Corp has a 35 per cent stake in BSkyB. He has stoked competition between his sons, saying: "So far, they are showing great promise. Lachlan is supervising companies which provided 60 per cent of last year's huge operating profit. James has just turned around the single most difficult situation we had in the whole company [at Star TV]. They are starting well, let's see."

The New York Times said at the weekend that Lachlan's relations with Peter Chernin, his direct boss and the most powerful executive at News Corporation who is not a member of the family, have been chilly. Mr Chernin, president of News Corporation, is expected to take over as its chief executive when Mr Murdoch stands down, and then to hand the reins to one of the family members.

Lachlan has also complained that his father dressed him down in front senior executives, The New York Times said. Several sources added that Lachlan believes his father was interfering directly in too many areas that he was supposed to be in control of, including 35 local US television stations that report to Lachlan. Mr Murdoch is understood to have held meetings and discussions with Jack Abernathy, president of the division, Fox Stations, without including his son.

That only left the New York Post - well known, but in business terms a less important part of the empire - as one of the only areas where Lachlan was sole charge. At the same time, James's star appears to have been rising. While most analysts in London think it is too early to tell what his lasting impact at BSkyB will be, he has overseen a revival of the satellite service's subscription numbers - though the cost was not welcomed by independent shareholders.

James is also thought to have influenced his father's thinking about the internet, which Mr Murdoch has identified as his top-most area of interest. James, 32, is now the most likely to inherit his father's mantle.

Mr Murdoch will also have to pay attention to outside factors. For the first time since building up the media giant, Mr Murdoch's control has been threatened by an outsider. Last year, another business titan, John Malone, swiftly built up an 18 per cent stake in News Corp, compared to Mr Murdoch's holding of 30 per cent. Mr Malone has said he has no interest in buying more stock, but Mr Murdoch is wary of his long-time business associate's ambitions. The two are currently discussing ways to unwind Mr Malone's holding.

Mr Murdoch does not have to hurry to resolve this problem, or to decide on his successor. He said at News Corporation's annual meeting in Adelaide two years ago, when he celebrated 50 years at its helm, that he would have to be "carried out" in a box. Given the uncertainties his company faces, it may be just as well that the 74-year-old has had a new lease of life married to his young wife.