(CNN) Millionaire real estate heir Robert Durst was "lying in wait" when he shot and killed his longtime friend because she "was a witness to a crime," prosecutors alleged Monday.

The evidence behind that accusation wasn't revealed in the Los Angeles County District Attorney's court filing, which charged Durst with first-degree murder. If he's convicted in the December 2000 killing of Susan Berman, prosecutors said, he could face the death penalty.

The charges, filed two days after FBI agents arrested Durst in New Orleans, set the stage for a new courtroom battle for a man who's no stranger to run-ins with the law.

Durst's alleged connections with Berman's death and two others became the focus of HBO's true crime documentary, "The Jinx."

He admitted to shooting and dismembering his neighbor but was acquitted of murder.

He was suspected in his first wife's disappearance, but no one could pin him to it.

And just before Berman, his longtime confidante, was going to speak to investigators about his wife's case, she was killed.

He's long denied any connection to her death or his wife's disappearance. But some say his mutterings picked up on a live microphone and broadcast in the HBO documentary make it sound like Durst could be changing his tune.

"What the hell did I do?" Durst says from a bathroom at the end of the documentary. "Killed them all, of course."

His attorney says not to read too much into those comments. But more on that later.

To understand the complexities of Durst's life -- and the deaths linked to it -- we have to start at the beginning:

His wife's disappearance

What we know: Durst amassed his fortune from his family's real estate business, Durst amassed his fortune from his family's real estate business, the Durst Organization , which owns a number of high-profile buildings in Manhattan.

His first wife, Kathie McCormack, was on her way to medical school in New York when she vanished in 1982.

"I put her on the train in Westchester to go into the city that evening. That was the last time I ever saw her," Durst testified in a separate case over a decade later.

McCormack had told her close relatives and friends that her husband had begun to abuse her physically. Sworn affidavits by her sister, an attorney and a family friend said that McCormack had told them that she was physically assaulted by Durst during their marriage.

Despite a cloud of suspicion over the years, Durst has never been arrested in the disappearance.

The case inspired the 2010 movie "All Good Things," which starred Ryan Gosling and Kirsten Dunst. Though Durst disputed the film's implication that he'd killed his wife, he praised the movie to The New York Times and said parts of it made him cry.

What we don't know: What actually happened to McCormack. What actually happened to McCormack. The New York Times said she has been declared legally dead.

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His friend's shooting death

What we know: Crime writer Susan Berman was a longtime friend of Durst's.

She'd helped handle his public relations after his wife's disappearance and also had plenty of troubles of her own. She'd written books about her family's mafia ties and was facing financial troubles

In 2000, when investigators reopened the 1982 disappearance case of Durst's first wife, they made plans to visit Berman in Los Angeles.

"She was a confidante of Robert Durst. She knew him well," CNN's Jean Casarez said. "And it was just days before investigators were to fly out to California to talk with her about what she may have known about the disappearance of Kathleen Durst that she was shot execution-style in her living room."

Fast forward 15 years, to this past weekend: Durst's arrest was in connection with Berman's death. (See below.)

What we don't know: We don't know whether Durst was the person who sent an anonymous letter to police telling them there was a body in Berman's home.

A police handwriting analysis said the writing on that card looked like Durst's, author Miles Corwin told CNN in 2004. But even with that, at the time, Corwin said police didn't have enough evidence to arrest Durst. So what's changed?

In "The Jinx," Berman's stepson reveals a letter from Durst he found among her possessions.

"You look at the letter, and the handwriting is astonishingly similar," said Michael Daly, a special correspondent for The Daily Beast.

His neighbor's dismemberment

What we know: In 2001 -- almost two decades after his wife's disappearance and after Berman's killing in late December 2000 -- millionaire Durst was living in the coastal Texas city of Galveston.

Durst testified that he hid out in Galveston and posed as a mute woman because he was afraid as he faced increasing scrutiny, Court TV reported at the time.

He got into a scuffle with his neighbor, Morris Black, and admitted to shooting and killing him.

Prosecutors said Durst planned Black's killing to steal his identity. Defense attorneys said Black sneaked into Durst's apartment, and Durst accidentally shot him as both men struggled for a gun.

Durst testified he panicked and decided to cut up Black's body and throw away the pieces.

What we don't know: Why Durst chose Pennsylvania to escape to after shooting and dismembering his neighbor.

He had jumped bond and almost got away -- if not for a sandwich that the heir stole from a store. He was captured in Pennsylvania for shoplifting, even though he had hundreds of dollars in his pocket.

His weekend arrest

What we know: Durst is now accused of killing Berman, the crime writer.

Authorities found him Saturday at a New Orleans hotel, where he was staying under a false name and was carrying a fake driver's license, according to a law enforcement official who's been briefed on the case. Durst had a Smith & Wesson .38-caliber revolver on him when he was arrested, according to New Orleans Police Department records.

He'd paid for the hotel in cash, and authorities believe he was preparing to leave the country and flee to Cuba, the official said.

Investigators found marijuana and a "substantial" amount of cash in Durst's hotel room, a source familiar with the investigation told CNN.

Police said they arrested Durst "as a result of investigative leads and additional evidence that has come to light in the past year."

The Los Angeles County District Attorney's Office on Monday charged him with first-degree murder. In New Orleans, he's also facing felony firearms and drug charges.

What we don't know: What the new evidence is that led authorities to arrest Durst, why they arrested him when they did and when he'll be taken to Los Angeles.

Susan Criss, a former Texas District Court judge who presided over the 2003 murder trial, told CNN that producers of "The Jinx" gave all the evidence they uncovered to police, and it's likely Durst's statements on the show are part of the case against him.

"That case has been several years in the making," she said. "The investigation has been going on. The making of the cases has been going on. And I think these are pieces of evidence that are going to be used, and they're going to be very powerful pieces of evidence."

But that doesn't mean investigators only learned about evidence as the show aired, she said.

"They turned over the handwriting sample a couple years ago, at least two or three years ago," she told CNN. "They told me when they did it. The police had it. The police didn't just learn this when they watched television. They've had that."

Dick DeGuerin, a longtime attorney for Durst, told The Los Angeles Times he believes the arrest was deliberately timed to the HBO documentary's finale, which aired on Sunday.

"Do I think this is a coincidence? Hell, no," he said. "There has been rumor, innuendo and speculation for a number of years, and now we're going to get our day in court on this."

Once that day comes, prosecutors said Monday that Durst could face the death penalty if convicted.

He waived his right to fight extradition to Los Angeles during an appearance Monday before a New Orleans Magistrate Court. But Durst remains in jail in New Orleans, where he was booked Monday on charges of being a felon in possession of a firearm and possession of a firearm with a controlled substance. That could delay his extradition.

The Los Angeles County District Attorney's Office says he'll be brought back to Los Angeles for arraignment "at a future date."

Durst's lawyers deny that he had anything to do with Berman's death and say they're eager for him to go to Los Angeles.

"Bob Durst didn't kill Susan Berman," DeGuerin told reporters Monday. "He's ready to end all the rumor and speculation and have a trial."

His puzzling comments

What we know: The HBO documentary series "The Jinx" aired in six episodes, ending Sunday.

Immediately after the finale's last shot, Durst went into the bathroom, apparently not realizing his microphone was still on.

"There it is. You're caught," he said.

He then rambled a series of seemingly unrelated sentences before saying, "He was right. I was wrong."

Then, the most intriguing remarks: "What the hell did I do? Killed them all, of course."

What we don't know: What did those words really mean?

Criss told CNN that it wasn't the first time Durst made statements that seemed to incriminate himself while being recorded.

"In our trial, he had been recorded on the phone talking to his wife and friends, making a lot of admissions, and the state never used that," she said. "But he was aware that he had been recorded, saying things that could implicate him in the murder we were trying. Earlier in those interviews, in a previous interview for that very program ('The Jinx'), there was a break where he was caught practicing his testimony. And so he realized, he knew he had a mic on. This is the third time he's made that mistake."

While the comments may appear incriminating, his attorney told Fox News' "Justice With Judge Jeanine" that the offhand remarks might not mean anything.

"Your honesty would lead you to say you've said things under your breath before that you probably didn't mean," attorney Chip Lewis said.

When asked for comment, HBO praised the series' director and producer in a statement Sunday.

"We simply cannot say enough about the brilliant job that Andrew Jarecki and Marc Smerling did in producing 'The Jinx,' " said HBO, which is owned by Time Warner -- the parent company of CNN. "Years in the making, their thorough research and dogged reporting reignited interest in Robert Durst's story with the public and law enforcement."

Jim McCormack, the brother of Durst's first wife, said he's glad Durst's ability to avoid conviction may be unraveling.

"The dominoes of justice are now starting to fall," he said. "Through our faith, hope and prayers the last domino will bring closure and justice for Kathie."