Over the years, William R. Ponsoldt had earned tens of millions of dollars building a string of successful companies. He had renovated apartment buildings in the New York City area. Bred Arabian horses. Run a yacht club in the Bahamas, a rock quarry in Michigan, an auto-parts company in Canada, even a multibillion-dollar hedge fund.

Now, as he neared retirement, Ponsoldt, of Jensen Beach, Florida, had a special request for Mossack Fonseca, a Panama-based law firm well placed in the world of offshore finance: How could he confidentially shift his money into overseas bank accounts and use them to buy real estate and move funds to his children?

“He is the manager of one of the richest hedge funds in the world,” a lawyer at Mossack Fonseca wrote when the firm was introduced to Ponsoldt in 2004. “Primary objective is to maintain the utmost confidentiality and ideally to open bank accounts without disclosing his name as a private person.”

In summary, the firm explained: “He needs asset protection schemes, which we are trying to sell him.”

Thus began a relationship that would last at least through 2015 as Mossack Fonseca managed eight shell companies and a foundation on the family’s behalf, moving at least $134 million through seven banks in six countries — little of which could be traced directly to Ponsoldt or his children.

These transactions and others like them for a stable of wealthy clients from the United States are outlined in extraordinary detail in the trove of internal Mossack Fonseca documents known as the Panama Papers. The materials were obtained by the German newspaper Suddeutsche Zeitung and the International Consortium of Investigative Journalists, and have been shared with The New York Times.

Federal law allows U.S. citizens to transfer money overseas, but these foreign holdings must be declared to the Treasury Department, and any taxes on capital gains, interest or dividends must be paid — just as if the money had been invested domestically. Federal officials estimate that the government loses between $40 billion and $70 billion a year in unpaid taxes on offshore holdings.

Experts in federal tax law, money laundering and offshore accounts — asked by The Times to examine certain documents or at least to identify legal issues raised by the money management techniques that Mossack Fonseca advocated — said the law firm at times had come up with creative, but apparently legal, strategies to save clients money.

While the experts were reluctant to declare that the law firm or its clients had broken any laws given that no charges have been filed, they said they were surprised at how explicitly Mossack Fonseca had offered advice that appeared carefully crafted to help its clients evade U.S. tax laws.

The firm’s U.S. client list does not appear to include the sort of high-profile political figures who have emerged from reporting on the Panama Papers in many other countries.

But the services offered by Mossack Fonseca, with 500 employees in more than 30 offices worldwide, were in high demand by the rich and famous in the United States.

In 2001, Sanford I. Weill, then chief of Citigroup, set up an offshore account called April Fool for his yacht. Alfonso Soriano, a former Major League Baseball All-Star player with the New York Yankees and other teams, had a Panamanian corporation created for him. John E. Akridge III, a leading real estate developer in Washington, flew to Panama to meet with Mossack Fonseca lawyers, who created in 2011 the Cyclops Family Foundation in Panama, along with a related bank account.

A spokesman for Weill said the accounts were used for legitimate purposes, and “appropriate disclosures were filed.” Akridge and Soriano did not respond to repeated requests for comment.

Few U.S. clients, the records show, demanded and received as much attention as Ponsoldt and two of his children, Tracey and Christopher, each of whom was assigned a secret email account and a code name — “father,” “daughter” and “son.” Mossack Fonseca’s “VIP service” consisted of everything from securing lunch reservations at a popular French bistro in Panama City to pressing the government to make an exception and grant Ponsoldt and his wife Panamanian passports.

Over the years, tens of millions of dollars flowed into a series of shell companies — Escutcheon Investment, with its money at the Banca Privada in the Pyrenees principality of Andorra; Probity Investments, with deposits at Andbanc Grup Agricol, also in Andorra; Royal Pacific Investments, with deposits at Balboa Securities in Panama; and Valdano Investments Group, with deposits at Berenberg Bank in Switzerland, among others, the bank records and other documents show.

The most important part of this elaborate structure was an entity called the Edenstone Foundation.

In secret meetings documented in the Panama Papers, Mossack Fonseca named the Ponsoldt family as the beneficiary, through the foundation, of the money placed in bank accounts around the world.

Among the early requests: confidentially transfer $800,000 from “father” to “son,” meaning moving the money to yet another offshore account — called LBFH of Panama — which Mossack Fonseca had set up on Christopher Ponsoldt’s behalf with bank accounts in Andorra and Panama.

Federal law generally limits such tax-free transfers between family members to $14,000 a year. But for this transfer, described as a “pre-inheritance distribution,” the documents give no indication that any U.S. gift taxes were paid, as would likely have been required, said Jack Blum, a lawyer and expert in international tax evasion who served for more than a decade as a consultant to the Internal Revenue Service.

Christopher Ponsoldt declined to comment. “I am sorry, I can’t help you,” he said before hanging up.

For another client, Mossack Fonseca offered a special service for a premium price.

Marianna Olszewski, the New York City-based author of “Live It, Love It, Earn It: A Woman’s Guide to Financial Freedom,” wanted to shift $1 million held by HSBC in Guernsey to a new overseas account. The catch? She did not want her name to appear anywhere near the transaction.

Ramsés Owens, then a partner who helped run the firm’s trust division, offered a solution.

Mossack Fonseca would locate what he called a “natural person nominee” in a “tax-convenient” jurisdiction to stand in for Olszewski as the owner of the account.

Olszewski approved the maneuver.

The use of a stand-in to hide the true ownership of an account is one of the remaining illegal ploys favored by Americans today as international banks, under pressure from the United States, demand proof of account ownership, said Jeffrey Neiman, a former federal prosecutor from Miami who specialized in criminal tax offenses, adding that he could not comment directly on this case. “The fact that a law firm was willing to do this legitimizes the process for their clients,” he said.

Many of the client files — like those for Weill, the banker; Soriano, the ballplayer; and Akridge, the developer — contain little information on the purpose of the offshore accounts or how they were used after they were set up, making it impossible, based on the records available, to assess whether they were used legitimately.

But the experts who reviewed some of the documents related to the Ponsoldts and Olszewski said the firm seemed to realize it was taking risks.

In 2013, Mossack Fonseca advised Olszewski to seek outside counsel and consider reporting herself to the IRS, warning of possible “severe” repercussions if she did not. The warning came in the wake of a Justice Department investigation of the role that certain Swiss banks had played in helping U.S. citizens evade federal taxes.

Olszewski took the firm’s advice, and belatedly disclosed her accounts to the IRS, the documents show. And by 2014, she asked Mossack Fonseca to shut down her accounts and offshore entities, which collectively held at least $1.7 million.

Mossack Fonseca sent a series of similar and increasingly dire warnings to the Ponsoldts in 2013 and 2014, telling them they had to provide a Swiss bank with documentation that they had paid all required U.S. taxes — or face possible investigation.

The records examined by The Times give no indication whether the Ponsoldts complied, and family members would not say when asked.