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The billionaire financier Leon Black, one of Wall Street’s most powerful executives, was facing questions from clients after Jeffrey Epstein was arrested last year on federal sex trafficking charges. The two men had known each other for decades, and investors of Mr. Black’s investment company, Apollo Global Management, wanted to know how close they had been.

Such questions were valid, Mr. Black said, according to a transcript of a call with analysts in July 2019. He said in a letter that same day to investors that he had had a “limited relationship” with Mr. Epstein, a convicted sex offender, and had consulted him “from time to time” on personal financial matters.

But their connection was deeper than Mr. Black let on: The two men often socialized and dined together, and Mr. Black was a lucrative client for Mr. Epstein over the final decade of his life.

Mr. Black wired Mr. Epstein at least $50 million in the years after Mr. Epstein’s 2008 conviction for soliciting prostitution from a teenage girl, according to documents reviewed by The New York Times and interviews with four people with knowledge of the transactions. The transfers included $10 million to a foundation started by Mr. Epstein and consulting fees that were sufficiently unusual to draw scrutiny from Deutsche Bank, where Mr. Epstein kept his accounts. Two of the people said the total amount sent by Mr. Black to Mr. Epstein could be as high as $75 million.

It was not clear what kind of services Mr. Epstein provided to Mr. Black, whose $9 billion fortune can buy him access to the best lawyers and accountants in the world. Mr. Epstein, though he styled himself as a “financial doctor” to wealthy clients, was a college dropout who had worked on Wall Street for just a few years, demonstrated no great skill as an investor and had no formal training in tax and estate planning.

“Mr. Black received personal trusts and estates planning advice as well as family office philanthropy and investment services from several financial and legal advisers, including Mr. Epstein, during a six-year period, between 2012 and 2017,” said Stephanie Pillersdorf, a spokeswoman for Mr. Black. “The trusts and estate planning advice was vetted by leading auditors and law firms.”

The business relationship ended in 2018 because of a “fee dispute” and Mr. Black stopped communicating with Mr. Epstein, she said.

“Mr. Black continues to be appalled by the conduct that led to the criminal charges against Mr. Epstein, and he deeply regrets having any involvement with him,” Ms. Pillersdorf said.

She added that Mr. Epstein did not do any work for Apollo, whose investors include some of the biggest public pensions in the country, large sovereign wealth funds and private foundations.

The fees from Mr. Black help explain a mystery about Mr. Epstein’s wealth: How a man who left behind an estate worth more than $600 million made money in the years after his most lucrative client, the billionaire retail magnate Leslie H. Wexner, cut him off.

Some of the payments from Mr. Black are described in an internal report by Deutsche Bank, which served as Mr. Epstein’s primary banker from 2013 into 2019. The report was provided to regulators who fined the German bank over the summer for its failure to catch numerous red flags in Mr. Epstein’s financial activities.

Portions of the report reviewed by The Times describe a payment of $22.5 million in 2017 by a company called BV70 LLC, which the bank said owned Mr. Black’s yacht, to Plan D, the company that managed Mr. Epstein’s Gulfstream jet. When an employee in Deutsche Bank’s anti-financial-crime division inquired about the payment, she was told by another bank employee that it was a fee for consulting services provided by Southern Trust Company, one of the dozens of entities Mr. Epstein operated in the Virgin Islands. There was no explanation for why the payment went to Plan D.

The Deutsche Bank report also shows that BV70 made a $10 million donation in 2015 to a charitable foundation started by Mr. Epstein, Gratitude America, which made several million dollars in grants while Mr. Epstein was casting himself as a philanthropist. BV70 also planned to make another payment of $10 million to Mr. Epstein for advisory work, according to the report, although it was unclear if that payment was ever made.

And in 2014, Mr. Epstein received several million dollars in fees from Narrows Holdings, a company that Mr. Black — the chairman of the Museum of Modern Art — has used to purchase much of his billion-dollar art collection, according to two of the people with knowledge of the transactions. The details of the services Mr. Epstein provided in exchange for those fees are also unclear.

Mr. Epstein portrayed himself as a financial guru to the wealthy, although for many years his chief client was Mr. Wexner, the founder of L Brands, which owns Victoria’s Secret. Mr. Epstein was first publicly accused of engaging in sex with underage girls in 2006, and Mr. Wexner said he cut ties with Mr. Epstein at the end of the following year. (Mr. Wexner said last year that Mr. Epstein had misappropriated “vast sums” from him; Mr. Epstein had returned at least $100 million to Mr. Wexner, The Times has reported.)

In 2008, Mr. Epstein pleaded guilty in Florida to a state prostitution charge with a minor and served 13 months in a state jail as part of a plea agreement with federal prosecutors — an arrangement that was kept confidential at the time. He kept a low profile for the next decade, but after an investigation by The Miami Herald drew attention to his plea deal, federal prosecutors in New York charged Mr. Epstein with sex trafficking in July 2019. His death the next month in a Manhattan jail cell was ruled a suicide.

Mr. Black knew Mr. Epstein for decades — in 1997 he made Mr. Epstein one of the original trustees of what is today called the Debra and Leon Black Foundation — and was among the high-profile figures who maintained ties with him following his prostitution arrest. They included Bill Gates, the Microsoft co-founder; Lawrence Summers, the former president of Harvard; James E. Staley, now the chief executive of Barclays; and the hedge fund manager Glenn Dubin and his wife, Eva.

Mr. Epstein frequently hosted Mr. Black at his New York mansion, usually meeting him for breakfast or lunch, according to four people familiar with their relationship. In 2012, while on a family vacation in the Caribbean, Mr. Black traveled by yacht to attend a cookout at Mr. Epstein’s private island residence in the U.S. Virgin Islands, two of the people said.

In 2011, Mr. Epstein’s financial advisory firm — Financial Trust — joined Mr. Black and members of his family in investing in a small emissions control company, Environmental Solutions Worldwide, where two of Mr. Black’s sons serve as board members. The company did not respond to requests for comment.

According to an archived version of one of Mr. Epstein’s websites, the men visited Mr. Black’s alma mater, Harvard, together. Although the university stopped accepting gifts from Mr. Epstein after his 2008 plea, according to a report by the university, Mr. Black had given at least $5 million to professors and Mr. Epstein’s staff members had “played a role in facilitating the Black donations.”

Business records from the Virgin Islands reviewed by The Times last year show how Mr. Epstein’s business suffered following his 2008 case. The conviction coincided with the fallout from the financial crisis, which cost Financial Trust $150 million. The company took in just $200,000 in fee income from 2008 to 2012 before closing down that year, the records show.

The same year, Mr. Epstein established a new business, Southern Trust Company, which he told territorial officials was primarily a DNA data-mining and genetic research provider with a “financial arm.” There’s little evidence the company — which had no scientists on its nine-member staff — ever did any research.

Southern Trust collected more than $180 million in fees between 2013 and 2017. (In 2018, the year Mr. Black said he cut ties with Mr. Epstein, Southern Trust reported no fee income.)

The attorney general of the Virgin Islands, Denise N. George, filed a civil forfeiture lawsuit against Mr. Epstein’s estate this year, claiming that Mr. Epstein had deceived officials to get Southern Trust a lucrative tax break and used his island retreat to engage in sex trafficking. Ms. George’s offices said in court filings that she intended to serve subpoenas on Mr. Black and several of his business entities. (Ms. George has said she intends to serve a subpoena on Mr. Dubin as well.)

Mr. Black’s representatives have been gathering documents to hand over to the attorney general’s office. Mr. Black was prepared to cooperate with Ms. George’s request, Ms. Pillersdorf said.