John and Laura Overdeck's divorce is giving the world a peek into the lives of the ultrarich, and the breadth of the onetime couple's enormous wealth at stake in a New Jersey courthouse.

A Wall Street Journal article this week laid out the staggering sums being cited in the divorce trial, which could also influence a power struggle atop Two Sigma, the quant trading powerhouse John Overdeck co-founded in 2001. Lawyers for Laura Overdeck are pushing the judge overseeing the trial to make more details public, including those from the couple's tax returns and their various trusts.

The judge has repeatedly reprimanded Laura Overdeck's lawyer for citing nonpublic figures in court.

Laura Overdeck on Wednesday sat by her legal team in the light-wood-paneled courtroom in Newark, N.J. wearing a gray-and-white striped jacket, white slacks and chunky blue heels. She has been barred from testifying or introducing witnesses because of violations during discovery.

John Overdeck, clad in a navy-blue suit, light blue shirt and no tie, has been questioned on the witness stand this week by his estranged wife's attorney. He sipped from a bottle of organic green tea during the cross-examination.

Here are highlights from the trial, which could drag on for months.

Wanted: A cash payout

The biggest asset at the center of the fight is John Overdeck's stake in Two Sigma. Laura Overdeck's lawyer estimates the value of that stake at $6.2 billion, and says her client wants 35% of that, or $2.17 billion. His side says his stake is worth $4.9 billion.

Laura Overdeck's lawyer clarified this week that her client isn't angling for influence over Two Sigma, but rather wants a cash payout. John Overdeck said his primary concern with regard to the firm was maintaining voting parity with his co-founder David Siegel, with whom he is locked in a bitter feud.

"But if there were an award in this case that caused me to liquidate that interest, the value that the firm would give me would not be anywhere near the fair value of that interest," Overdeck said Tuesday.

'A decent husband'

The acrimony between the two sides is apparent in the courtroom. The Overdecks rarely look at each other during the proceedings. John Overdeck once appeared to smile when the judge reprimanded Laura's lawyer. Laura Overdeck at times shook her head in response to John's answers on the stand.

Laura Overdeck is barred from testifying or introducing witnesses after the court found she obtained confidential emails from her husband's laptop, among other violations. The judge has also said Laura Overdeck's legal team can't introduce any evidence of the facts in the case.

John Overdeck's previous testimony has alluded to happier times. He has said on the witness stand that Laura Overdeck came to the firm's holiday parties for much of the marriage, and that he gave away copies of her Bedtime Math books to people at the firm.

"It showed me to be a decent husband," he said.

An $8 billion trust?

Laura Overdeck's lawyer, Theresa Lyons, appears to be trying to strategically maneuver around the court's restrictions on her client by pushing to make certain confidential documents public and slipping mentions of other nonpublic details into her questioning. There were also signs that Lyons might have been responding forcefully to the judge to lay the groundwork for an eventual appeal.

At one point Tuesday, Lyons was rebuked when discussing the couple's finances.

John Overdeck testified that he owned his stake in Two Sigma directly until transferring it to a revocable trust in 2007. He said he "didn't know off the top of my head" whether his wife would remain a beneficiary in the event of a divorce.

Lyons then questioned how John Overdeck could be unaware of the terms of a trust that "holds $8 billion."

That figure apparently wasn't supposed to be public, and prompted an objection from John Overdeck's lawyer. The judge called both lawyers to the bench.

"I just told counsel to be exceedingly careful about revealing confidential financial information," Judge Bruce Buechler said after they returned to their seats.

A family empire is questioned

Lawyers on Wednesday discussed when John Overdeck could retrieve belongings from the couple's Short Hills, N.J. home, where Laura Overdeck still lives. Lyons said the children shouldn't be present when that happened.

The judge noted the three children are now in college.

Later in the morning, questions about the family's charitable giving led to a testy and awkward exchange. Lyons asked John Overdeck whether the couple's giving improved the image of "the Overdeck family empire." He responded that he didn't think they had "an empire."

Lyons: "You control billions of dollars, right, sir?"

John Overdeck: "I control billions of dollars?"

Lyons: "You own billions of dollars."

John Overdeck: "I guess so, yes."

The lunch break

The judge gives a one-hour break for lunch. John Overdeck's legal team has been collecting lunch orders each morning and having food delivered to the courthouse from Hobby's Delicatessen, a legendary eatery near the courthouse.

A convenience store in the courthouse lobby has limited hot-food options, with offerings in recent weeks including a buffalo-chicken wrap and tilapia oreganata.