FBI agents arrested Durst at a New Orleans hotel Saturday 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 hearing today.
Durst gave an extensive interview to filmmaker Andrew Jarecki for the documentary "The Jinx: The Life and Deaths of Robert Durst."
His estranged and fearful relatives thanked authorities for tracking him down.
The Durst family is worth at least USD 4 billion, according to the Forbes list of richest Americans.
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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.
Berman, who was Durst's spokeswoman, was killed at her home as New York investigators prepared to question her in the unsolved 1982 disappearance of Durst's wife, Kathleen.
Last week's episode revealed a hand-written address on a letter that Durst had sent to Berman. The handwriting seems virtually identical to an anonymous letter alerting Beverly Hills police to a "cadaver" in Berman's home.
His lawyer, Chip Lewis, said he has no doubt his client's arrest was orchestrated in coordination 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 last night, Durst was asked about the similarities in handwriting. Later, filmmakers said Durst wore his microphone into the bathroom.
Durst then said, apparently to himself, "There it is. You're caught" and "What the hell did I do? Killed them all, of course."
After Berman's death, 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 neighbor, Morris Black, were found floating in Galveston Bay.