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Robert Durst was the subject of “The Jinx,” a six-part documentary series on HBO. Credit HBO

Since his first wife vanished more than three decades ago, Robert A. Durst, the eccentric and estranged son of one of New York’s most prominent real estate dynasties, has lived under the suspicious gaze of law enforcement officials in three states.

They have followed his path from New York City to Los Angeles, where one of his closest friends was found dead in her home in 2000. They have tracked him to Galveston, Tex., where he fled after investigators reopened the case of his wife’s disappearance, and where he posed as a mute woman and shot and dismembered a neighbor in 2001.

Mr. Durst was acquitted in the Texas killing, and was never arrested in the disappearance of his wife or the death of his friend. But on Saturday, he found himself in custody once again, arrested on a charge of murder as he walked into a New Orleans hotel he had checked into under a false name.

On Sunday night, in the final moments of the final episode of a six-part HBO documentary about him, “The Jinx: The Life and Deaths of Robert Durst,” Mr. Durst seemed to veer toward a confession that could lift the shroud of mystery that surrounds the deaths of three people over the course of three decades.

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Susan Berman, a close friend of Mr. Durst, right, in a photo provided by HBO. Credit Sareb Kaufman

“What the hell did I do?” Mr. Durst whispers to himself in an unguarded moment caught on a microphone he wore during filming. “Killed them all, of course.”

In the years since his wife, Kathleen Durst, disappeared in 1982 after spending the weekend at the couple’s country home in Westchester County, Mr. Durst has bounced in and out of jail for other crimes, cut ties with his family, remarried, and sued his brother for a $65 million share of the family fortune. Through it all, he has maintained his innocence in the disappearance of his wife, while also denying any role in the 2000 death of the Los Angeles friend, Susan Berman.

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