Nicholson, who returned from a holiday in London last week, resolved to “sort out” the estate at 12900 Mulholland Drive. The famous address, on the mountain road overlooking Los Angles, is where Nicholson cared for his friend Brando before his death.

The 69-year-old actor has been advised that it would be too expensive to restore the “derelict” house which has been beset by mould. Getting the mould out would be difficult. “It’s more likely that we will take the house down,” said Nicholson last week.

For safety reasons Nicholson will probably fill in the pool which, shortly before his death, Brando declared he would stock with electric eels to power his house and reduce his electric light bill.

In court records signed a year before his death, where an ailing Brando pleaded poverty after he was entangled in a child maintenance dispute, he described the house as a “one-bedroom bungalow with a den converted from a garage”. He called it Frangipani, after the cream and yellow flower beloved of Buddhists. The double Oscar winner’s assets were estimated by his executors at £11m, largely from the sale of Frangipani and Tetiaroa, Brando’s island near Tahiti in the south Pacific.

Yet Brando said he was also facing a mountain of debts in his later days including £4m of legal bills and interest payments unpaid since 1990 when his son Christian was arrested after killing a Tahitian man.

The star claimed to have spent all his advances, including a then-record £2.5m payment for 15 minutes of screentime in the 1978 Superman movie, and was so “cash poor” that he could not afford to repaint Frangipani or even change its burnt-out light bulbs.

Last year the house, about the size of a four-bedroomed home in Britain, was cleared by Christie’s which auctioned most of the clutter that it found in boxes and plastic bags, from Brando’s script for The Godfather to an exercise machine, for £1.3m.

His posthumous finances are still being untangled in a blizzard of writs. One woman is claiming £2,000 for a diamond ring she says she lost down the sink at Frangipani. Last month a former personal assistant, who claimed that Brando’s will was fraudulently changed days before he died to cut her out, initiated a £1.5m damages action against the estate.

The executors, including Michael Medavoy, the film producer, are raising money by licensing Brando products including a forthcoming Superman statue — “the first time Marlon Brando has been immortalised in plastic”. There is also one final performance to be released, a semi-fictional documentary called Citizen Brando.

The executors have sold Tetiaroa to Richard Bailey, a developer distrusted by Brando, who says he will turn the 13-island atoll into a luxury “eco-resort”.

Nicholson bought Frangipani shortly after Brando died on July 1, 2004 from lung failure. He wanted to ensure his own privacy and to respect Brando’s memory as one of Hollywood’s most influential stars. He also wanted to maintain it for Brando’s children, but they have shown little interest in spending time there.

Nearly everything owned by Brando has been destroyed or sold. Yet there is one fragment of the legacy still unaccounted for: the Oscar he received for On the Waterfront (1954).

Relatives believe he either lost it, gave it to a friend or, in a darker mood, hid the 13in statue from debt collectors. The gold-plated knight may yet emerge from Frangipani’s dust during the demolition.

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