Robert Durst, a millionaire from one of America's wealthiest families, has been arrested just before the finale of a serial documentary about his links to three sensational murders in which he said he "killed them all".

FBI agents arrested Mr Durst at a New Orleans hotel on a warrant from Los Angeles for the murder of a mobster's daughter 15 years ago, authorities said. He was ordered held without bond pending a court hearing.

Mr Durst gave an extensive interview to filmmaker Andrew Jarecki for the documentary The Jinx: The Life and Deaths of Robert Durst.

Mr Durst's estranged and fearful relatives thanked authorities for tracking him down.

"We hope he will finally be held accountable for all he has done," said his brother Douglas Durst in a statement. The Durst family is worth at least £2.7 billion, according to the Forbes list of richest Americans.

Mr Durst, 71, has always maintained his innocence in the 2000 murder of Susan Berman, whose father was an associate of Las Vegas mobsters Bugsy Siegel and Meyer Lansky.

Ms Berman, who was Mr Durst's spokeswoman, was killed at her home with a bullet to the back of her head as New York investigators prepared to question her in the unsolved 1982 disappearance of Mr Durst's wife Kathleen.

The climax of last week's episode revealed a hand-written address on a letter Mr Durst had sent to Ms Berman. The handwriting seems virtually identical to an anonymous letter alerting Beverly Hills police to a "cadaver" in Ms Berman's home. Even the word "Beverly" is misspelled as "Beverley" on both documents.

Mr Durst observes in the documentary only Ms Berman's killer could have sent the letter to police.

His lawyer Chip Lewis said he has no doubt his client's arrest was orchestrated in co-ordination with HBO's broadcast of the final episode. The Los Angeles Police said the arrest resulted from "investigative leads and additional evidence that has come to light in the last year".

In the finale, Mr Durst was asked about the similarities in handwriting. Later, filmmakers said Mr Durst wore his microphone into the bathroom.

Mr Durst then said, apparently to himself, "There it is. You're caught" and "What the hell did I do? Killed them all, of course."

The show ended and it was not clear whether producers confronted Mr Durst about the secretly recorded words, or what Mr Durst meant by them.

After Ms Berman's death, Mr Durst moved to Texas, where he lived as a mute woman in a boarding house until his arrest in 2001 after dismembered parts of the body of his elderly neighbour, Morris Black, were found floating in Galveston Bay.

Mr Durst then became a fugitive until he was caught shoplifting in Pennsylvania, even though he had $500 cash in his pocket and $37,000 in his rental car, along with two guns and marijuana.

Mr Lewis told the jury Mr Durst shot Mr Black in self-defence and had Asperger's syndrome. Despite admitting he used a paring knife, two saws and an axe to dismember Mr Black's body before dumping the remains, Durst was acquitted of murder.