“You can take the money in cash, you can do a bad investment; you can purchase something and not receive anything (an expensive piano, an expensive software),” Mr. Owens wrote. “You can receive an invoice from Panama or any other location and that would justify some of the outgoing moneys. You can also declare everything to the tax administration.

“Any decision you make, please be aware that you will have to sign a ‘disclaimer’ to us. We can only ‘suggest,’ but the final decision to take the money out of the country is fully yours, and under the professional opinion of someone in USA.”

This was the sort of menu sold to the Ponsoldt family — in a very big way.

Image William R. Ponsoldt in 1986. Mossack Fonseca managed eight shell companies and a foundation on his family’s behalf. Credit... via Arabian Horse World

William Ponsoldt, now 74, had come to Mossack Fonseca with hundreds of millions of dollars in assets, the firm’s staff estimated in “due diligence” memos that also laid out how he had become so wealthy.

“He has started off in the 70ties purchasing run-down apartment buildings in New York, in order to refurbish and sell them off,” noted one memo from 2007, shortly after the firm had started to handle the family’s investment accounts. “Having done this for a while he spread out to various businesses and his CV is the typical profile of a serial entrepreneur.” The memo went on to list nine businesses he had created, taken over or helped run, including Glas Aire Industries Group, an automotive parts supplier; Zeus Energy Resources, a Texas oil-drilling company; Regency Affiliates, which owned a Michigan rock mine; and Pegasus Ranch, one of the country’s largest Arabian-horse-breeding operations.

Few American clients, the records show, demanded and received as much attention as Mr. 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 “V.I.P. 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 Mr. Ponsoldt and his wife Panamanian passports.