Robert F. Kennedy Jr. has agreed to pay his late wife's lawyers $278,000 in fees for representing her during bitterly contentious divorce proceedings in the years before she took her own life.

The agreement came during a brief, closed-door hearing in New York State Surrogate Court in White Plains on Wednesday as Mary Richardson Kennedy's lawyers tried to get a neutral third party -- Westchester County Public Administrator George Lambert -- to oversee the estate.

"Robert Kennedy has acknowledged finally that he owes the fees to Mrs. Kennedy's lawyers," said Patricia Hennessey, one of Mary Richardson Kennedy's divorce lawyers.

Mary Kennedy's lawyers say they're owed more than $278,000 and that Robert F. Kennedy Jr. was under court order to pay them, but has not. The lawyers claim that he stopped paying his wife's bills several months before she hanged herself in May and was squeezing her financially.

Also Wednesday, state Supreme Court Judge Anthony Scarpino said he will likely appoint the couple's eldest son -- John Conor Kennedy, 18 -- as administrator of the estate along with Faith Miller, the attorney who represented the four children's interests during the two-year divorce proceedings, which remained unresolved at the time of Mary Kennedy's death.

John Conor Kennedy, wearing a blue suit and powder blue tie, said nothing during the proceedings but conferred privately with his lawyers.

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He turned 18 on Tuesday, making him eligible to serve as administrator. In court papers, he listed addresses in Hyannisport, Mass., and Chevy Chase, Md.

On the way out, he noticed his mother's younger sister, Martha Richardson, sitting in the courtroom and stopped to give her a hug.

Martha Richardson sat in the gallery with her lawyer, Kerry Lawrence. Later, she said she's not sure whether she will ask the court to be named administrator of her sister's estate and challenge her nephew's appointment.

"I'm not quite prepared to make a decision about that yet," Richardson said outside the courtroom.

Mary Kennedy, 52, did not make out a will before her death, leaving the decision about who will oversee her estate up to Scarpino. Typically, that role falls to the next of kin.

Her sister said her family, which has sparred with the Kennedys over her sister's burial plot, has not decided what their next move will be.

"I think there are a lot of questions remaining about my sister's death," said Richardson, who lives in Washington, D.C. She declined to elaborate.

It's unclear how much money, if any, is in Mary Richardson Kennedy's estate or whether she held assets separately from her husband, her lawyers say.

At the time of the suicide, Robert F. Kennedy Jr. had temporary custody of their four children while he sought permanent custody of Conor; Kyra, 17; Fin, 15; and Aiden, 11.

In 2010, the couple's troubles went public when he filed for divorce and she was arrested twice, once for allegedly driving while intoxicated and a second time for allegedly driving under the influence of prescription drugs. Her depression and alcohol usage reportedly deepened as Robert F. Kennedy Jr. began dating "Curb Your Enthusiasm" actress Cheryl Hines.

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Her death started an ongoing feud between her siblings and Robert F. Kennedy Jr. over the burial of her body and ownership of the Bedford estate, which she had renovated as a model of eco-friendly architecture.

By agreeing to pay his wife's legal bills, Kennedy headed off a potentially bruising court battle with his late wife's lawyers.

In court papers, they cast Kennedy as a "tenacious and devious adversary" who hid assets from his wife, stripped her of financial support and tried to wrest away custody of their four children.

"Mr. Kennedy engaged in a scorched-earth litigation approach that required our firm and Parente Beard (business and accounting consultants ) to put in many hours in defense of Ms. Richardson Kennedy's equitable distribution, support and custody claims," attorney Peter Bienstock wrote to Scarpino in court papers last month.

Bienstock claims Kennedy restricted his wife's access to credit cards and "cut off her access to cash," the court papers say.

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"Unfortunately, the last months of Ms. Richardson Kennedy's life were full of daily financial challenges, directly attributable to Mr. Kennedy's litigation tactics," Bienstock wrote.

Weeks before Mary Kennedy's death, a Brooklyn process server turned up at the door of her Bedford home and handed her a lawsuit filed by American Express demanding $32,000 in overdue bills.

That lawsuit was dropped last month, court papers show. It's not clear who picked up the tab.

Bienstock claims that RFK Jr. stepped up the pressure on his wife in January 2012, trying to get her to back down from her demands for shared custody and a fair share of the company's assets, court papers say.

Bienstock said she felt trapped because she had not worked in years and was dependent on her husband for financial support.

"Ms. Richardson Kennedy ... had no independent source of income and was entirely financially dependent on Mr. Kennedy, not only for counsel and expert fees, but also for basic expenses, including medical bills, household utilities and groceries as well as the children's expenses," Bienstock wrote.

By court order, RFK Jr. was not allowed to see the details of the expenses that his wife's lawyers incurred, Hennessey said Wednesday.

"He had no right to see the details of those bills," Hennessey said.

If there is a dispute over how much is owed, it will be resolved by a Supreme Court judge who handles divorce matters, she said.

RFK Jr.'s lawyers did not comment outside the courtroom Wednesday and could not immediately be reached for comment afterward.