Director Andrew Jarecki explores the mysterious deaths surrounding Robert Durst, above, in HBO’s new docuseries “The Jinx.” (Photo courtesy of HBO)

Months ago — seemingly all at once and on the most conspicuously literate end of the pop-culture spectrum — people became obsessed with a podcast called “Serial,” in which a reporter, Sarah Koenig, meticulously and even obsessively combed through the details of a Baltimore high school student’s murder in 1999, hoping to discover if the man convicted of the crime really did commit it.

The surprise popularity of “Serial” had less to do with the garden-variety crime at the center of its story than how Koenig chose to build out her story.

Acting against ancient journalism-school instincts — get the important stuff up high; nail the story down before you publish or broadcast — “Serial” instead invited its listeners on a wandering ride-along as Koenig tracked down leads and asked questions both factual and existential. Those who find this style maddening were far outnumbered, it would appear, by listeners who loved having the story served to them in thoughtful, baby-spoon bites. Fans even calmly accepted the open-endedness of the last episode, when Koenig failed to crack the case.

All of which is to say you can’t help but think of “Serial” while enjoying director Andrew Jarecki’s fascinating and creepy “The Jinx: The Life and Deaths of Robert Durst,” a six-part ­documentary series that begins Sunday evening on HBO.

Similarly served in morsels rather than as a meal of more than three hours, “The Jinx” follows the trials and travails of Durst, now 71, an heir to a Manhattan ­real estate fortune. In the fall of 2001, Durst was arrested in connection with the murder of his neighbor in a cheap apartment house in Galveston, Tex. The victim’s body parts — minus the head — were found in trash bags in the bay. Durst’s arrest, as it happened, was one of tabloid New York’s first distractions from the Sept. 11, 2001, terrorist attacks.

Acquitted in 2003 (Asperger syndrome was part of his defense), Durst had admitted in court to sawing and hacking apart the victim’s body; he later served time for a bond violation and evidence tampering. He lives comfortably in New York.

But that’s not all. Durst’s pretty wife, Kathie, mysteriously vanished in 1982 and is still missing. One of his friends, who also knew his wife, was murdered in 2000. Although Durst has never been charged in either case, suspicions still swirl around all of it.

So there’s a lot of material to unpack here, in whatever elliptically tantalizing order a documentary filmmaker might ­prefer — but is it interesting? I suggest that a fascination for Durst’s guilt or innocence dissipates considerably the farther one gets from Page Six and the 212 area code.

Despite that, “The Jinx” is as irresistible as a bowl of peanuts. Jarecki, who made the memorably unsettling 2003 documentary “Capturing the Friedmans,” also made a fictional feature film (2010’s “All Good Things”) that was loosely based on Durst’s brushes with the law. Weirdly enough, that was the catalyst for Durst to contact Jarecki and invite him — and his camera — in for a project that would wind up taking several years to finish.

Although only parts 1 and 2 were available to critics when I had to file this review, it’s hard to deny that “The Jinx” easily hooks viewers in, so long as they can endure the gruesomeness of the Galveston crime-scene photos in the first episode. The beady-eyed Durst is a wily but generous interview subject, but where “The Jinx” really succeeds is in its fantastic attention to pace and detail, particularly in reenactments that are far and away better than what we usually see on “48 Hours,” et al. (Another nice touch: a soundtrack performed on a saw.)

Even with all the intelligent window dressing, that’s really all “The Jinx” boils down to: another strange story of an American weirdo who kept a few unlucky small-town homicide detectives very, very busy. In a room full of TV critics and reporters a few weeks ago, Jarecki all but promised that “The Jinx” would reach a satisfying conclusion in episode 6.

When it comes to documentaries and scripted dramas these days (and now podcasts), I don’t know what a “satisfying” conclusion really is anymore. It seems that ambiguity is always part of the package now.

The Jinx: The Life and Deaths of Robert Durst

(40 minutes; first of six parts) premieres Sunday at 8 p.m. on HBO.