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WASHINGTON — Even as Apple became the nation’s most profitable technology company, it avoided billions in taxes in the United States and around the world through a web of subsidiaries so complex it spanned continents and surprised experts, a congressional investigation has found.

Some of these subsidiaries had no employees and were largely run by top officials from the company’s headquarters in Cupertino, Calif., according to congressional investigators. But by officially locating them in places like Ireland, Apple was able to, in effect, make them stateless — exempt from taxes, record-keeping laws and the need for the subsidiaries to even file tax returns anywhere in the world.

In 2011, for example, one subsidiary paid Ireland just one-20th of 1 percent in taxes on $22 billion on pretax earnings from various operations; another did not file a corporate tax return anywhere and has paid almost nothing on $30 billion in profits since 2009.

“Apple wasn’t satisfied with shifting its profits to a low-tax offshore tax haven,” said Sen. Carl Levin, D-Mich., chairman of the Senate Permanent Subcommittee on Investigations. “Apple sought the holy grail of tax avoidance. It has created offshore entities holding tens of billions of dollars while claiming to be tax resident nowhere.”

Sen. John McCain, R-Ariz., the ranking member on the panel, added: “Apple claims to be the largest U.S. corporate taxpayer, but by sheer size and scale, it is also among America’s largest tax avoiders.”

Overall, Apple’s tax-avoidance efforts shifted at least $74 billion from the reach of the Internal Revenue Service between 2009 and 2012, the investigators said. That cash remains offshore, but Apple could still have to pay taxes on it to American authorities if the company were to return the money to its coffers in the United States.

Still, the findings about Apple were remarkable both for the enormous amount of money involved — tens of billions of dollars — and the audaciousness of the company’s assertion that its subsidiaries are beyond the reach of any taxing authority because they are “stateless.”

“There is a technical term economists like to use for behavior like this,” said Edward Kleinbard, a law professor at the University of Southern California in Los Angeles and a former staff director at the Congressional Joint Committee on Taxation. “Unbelievable chutzpah.”

And while Apple’s strategy was unusual in its scope and effectiveness, it underscores how riddled with loopholes the U.S. corporate tax code has become, critics say. It also shows how difficult it will be for Washington to overhaul the tax system and shut these loopholes down.

“It’s like playing Whac-A-Mole,” said one congressional staff member.

Although the Senate examination of Apple was started by a Senate subcommittee more than 18 months ago, investigators discovered one major subsidiary in Ireland only Sunday night. A Senate hearing on the issue is scheduled for Tuesday and will include testimony by Apple’s chief executive, Timothy Cook.

Apple declined to comment, except to make available a text of the testimony Cook is expected to provide.

Cook is expected to emphasize that Apple is most likely “the largest corporate income tax payer in the U.S., having paid nearly $6 billion in [U.S.] taxes” in the past fiscal year. “Apple does not use tax gimmicks,” Cook is expected to testify.

He is expected to seek to rebut the congressional findings by arguing some of Apple’s largest subsidiaries do not reduce Apple’s tax liability, and to argue in favor of a sweeping overhaul of the U.S. corporate tax code — in particular, lowering rates on companies moving foreign overseas earnings back to the United States. Apple now assigns more than $100 billion to offshore firms.

Atop Apple’s offshore network is a subsidiary named Apple Operations International, which is incorporated in Ireland but keeps its bank accounts and records in the United States and holds board meetings in California.

Because the United States bases residency on where companies are incorporated, while Ireland focuses on where they are managed and controlled, Apple Operations International was able to fall between the cracks of the two countries’ jurisdiction.

Apple Operations International has not filed a tax return in Ireland, the United States or any other country over the past five years. It had income of $30 billion between 2009 and 2012. By shuttling revenue between international subsidiaries, Apple sidestepped paying taxes, investigators said.

Despite Apple’s public contention that it pays substantial amounts in taxes to the IRS, the Senate’s permanent subcommittee on investigations also found evidence that the company turned over substantially less money to the government than its public filings indicated.

While the company cited an effective rate of 24 percent to 32 percent in its disclosures, its effective tax rate was 20.1 percent, based on the panel’s findings. And for a company of Apple’s size, the difference was substantial — more than $8 billion in 2009, 2010 and 2011.

Because of these strategies, tax experts say, the government is forced to rely more heavily on payroll taxes and individual income taxes to finance its operations. For example, in 2011, individual income taxes contributed $1.1 trillion to federal coffers, while corporate taxes added up to $181 billion.