As an indication of how well-cloaked shell company ownership is, it took The Times more than a year to unravel the ownership of shell companies with condos in the Time Warner Center, by searching business and court records from more than 20 countries, interviewing dozens of people with close knowledge of the complex, examining hundreds of property records and connecting the dots from lawyers or relatives named on deeds to the actual buyers.

Image COURAGE UNDER FIRE

TOM BRADY

The New England Patriots quarterback who bought his 74th-floor condo in 2006 through a trust, Courage Under Fire.

Yet in some cases it is nearly impossible to establish with certainty the source of money behind shell companies. Purchasers can register shell companies in the names of accountants, lawyers or relatives. Purchases are often made not just by individuals but on behalf of groups of investors or numerous family members, further obscuring the origin of the funds. What is more, ownership of shell companies can be shifted at any time, with no indication in property records.

The high-end real estate market has become less and less transparent — and more alluring for those abroad with assets they wish to keep anonymous — even as the United States pushes other nations to help stanch the flow of American money leaving the country to avoid taxes. Yet for all the concerns of law enforcement officials that shell companies can hide illicit gains, regulatory efforts to require more openness from these companies have failed.

“We like the money,” said Raymond Baker, the president of Global Financial Integrity, a Washington nonprofit that tracks the illicit flow of money. “It’s that simple. We like the money that comes into our accounts, and we are not nearly as judgmental about it as we should be.”

In some ways, officials are clamoring for the foreign wealthy. In New York, tax breaks for condominium developments benefit owners looking for a second, or third, residence in one of Manhattan’s premier buildings. Mayor Michael R. Bloomberg said on his weekly radio program in 2013, shortly before leaving office: “If we could get every billionaire around the world to move here, it would be a godsend.”

Among the Time Warner Center owners identified by The Times are at least 17 billionaires on Forbes magazine’s annual list of the world’s richest people. Five of the world’s leading art collectors own units, as do eight people who have been chief executives of major companies. And it has been home to numerous celebrities, including the singers Jimmy Buffett and Ricky Martin, the New England Patriots quarterback Tom Brady and the talk show host Kelly Ripa.

A look behind some doors revealed more complicated tales.

Units 72B and 51E are owned by the Amantea Corporation, which The Times traced to a mining magnate named Anil Agarwal. His company was fined for polluting a major river near a copper mine in Zambia, which sickened nearby residents. And judicial committees in his native India determined that his company had violated the land rights of an indigenous tribe near a proposed mine.