Mr. Leitner, a retired computer programmer, was not pleased to learn that his rent had been artificially inflated. Like other tenants interviewed by The Times, he wants that money back.

“If they passed on phony costs to tenants, they should lower our rents,” he said.

The Times’s investigation of the Trump family’s finances, based on a vast trove of tax returns and confidential financial records, found that Donald Trump, contrary to his lifelong claim of being a self-made billionaire, received the equivalent today of at least $413 million from his father.

That fortune was greatly increased by dubious schemes — including instances of outright fraud — designed to dodge gift and estate taxes, the investigation found. Mr. Trump was a central player in the formulation of those strategies, which included grossly undervaluing his father’s apartment complexes in tax filings, interviews and records showed. He also received tens of millions of dollars in gifts from his father that were disguised as loans or business investments.

Mr. Trump and his brother Robert did not respond to requests for comment for this article. But in a written statement for The Times’s original piece, one of the president’s lawyers, Charles J. Harder, said that “there was no fraud or tax evasion by anyone,” and that Mr. Trump had delegated tax matters to relatives and tax professionals.

The most overt fraud uncovered by The Times involved the sham corporation, All County Building Supply & Maintenance, created by the Trumps in 1992. It appeared, on paper at least, to be a purchasing agent for Fred Trump’s buildings.

In reality, the creation of All County did not change how Fred Trump’s business functioned. He and his executives continued to negotiate prices for everything from roofs to window cleaner, but vendors began receiving checks from an All County bank account. Fred Trump’s apartment buildings then reimbursed All County, with an extra 20 to 50 percent tacked on.

All County was owned by Donald Trump, his three siblings and a cousin. In some years, the amounts distributed to each Trump sibling ballooned to nearly $1 million, records obtained by The Times show.