Apple reacted to widespread criticism of its tax affairs by secretly shifting key parts of its empire to Jersey as part of a complex rearrangement that has allowed it to keep an ultra-low tax rate, according to an analysis of Paradise Papers documents.

The move affected two of its most important subsidiaries, one of which is thought to hold the key to a company cash pile worth more than $250bn (£190bn).

Over the past three years, Apple has reported paying very low tax rates on its profits outside the US – not much more than previously. But this remains significantly lower than all the major markets where its phones, iPads and desktop computers are sold – and less than half the rate in Ireland, where the company has many of its subsidiaries.

Though Apple has done nothing illegal, the disclosure is likely to raise fresh questions for the technology company, which has been forced to defend its tax affairs. It may also prompt awkward questions about the nature of the new tax rules introduced by the Irish government and their timing.

Apple refused to answer detailed questions, but defended the new arrangements and said they had not decreased the company’s tax payment anywhere in the world.

“The debate over Apple’s taxes is not about how much we owe but where we owe it. We’ve paid over $35bn in corporate income taxes over the past three years, plus billions of dollars more in property tax, payroll tax, sales tax and VAT,” it said.

“We believe every company has a responsibility to pay the taxes they owe and we’re proud of the economic contributions we make to the countries and communities where we do business.”

Edward Kleinbard, a former corporate lawyer who is a professor of tax law at the University of Southern California, told the International Consortium of Investigative Journalists: “US multinational firms are the global grandmasters of tax avoidance schemes that deplete not just US tax collection, but the tax collection of almost every large economy in the world.”

Tim Cook announcing the new iPhone 7 in 2016. Photograph: Marcio Jose Sanchez/AP

Documents in the Paradise Papers show how Apple began to consider its options in 2014 following criticism of the way it was doing business through Ireland. A year earlier, a bipartisan US Senate committee had pilloried the company for seeking “the holy grail of tax avoidance”. It highlighted practices that had saved Apple from paying billions of dollars over decades.

The 40-page analysis published in May 2013 described how Apple had incorporated one of its main subsidiaries, Apple Operations International (AOI), in Ireland in 1980. But the subsidiary had “no employees and no physical presence [in Ireland] … and holds its board meetings in California”.

Senators highlighted two other Apple subsidiaries in Ireland, Apple Sales International (ASI) and Apple Operations Europe (AOE), which were also in effect “stateless”. The scale of the tax avoidance was huge, the senators said. They described Apple’s arrangements as “a gimmick”.

Senators were so infuriated by the arrangements that they accused Apple of exploiting the gap between the two nations’ tax laws and creating a “byzantine tax structure” that was inexcusable. One of the report’s authors, the Democratic senator Carl Levin, said Apple had “created offshore entities holding tens of billions of dollars while claiming to be tax resident nowhere”.

The Republican senator John McCain said: “Apple claims to be the largest US corporate taxpayer, but by sheer size and scale it is also among America’s largest tax avoiders … [It] should not be shifting its profits overseas to avoid the payment of US tax, purposefully depriving the American people of revenue.”

Senator John McCain. Photograph: Aaron P Bernstein/Reuters

In the months that followed the publication of the report, and with the European commission also starting to scrutinise Apple’s tax arrangements, Ireland came under pressure to change its tax rules and new proposals were announced in October 2013.

The Irish government said companies incorporated in Ireland, such as Apple’s subsidiaries, would be able to avoid owing corporation tax only if they could show they were being “managed and controlled in another jurisdiction” where they would be liable for tax.

The announcement left Apple with a stark choice. It either had to acknowledge the subsidiaries were being run from the US, meaning they would have to pay American taxes. Or it had to find a new jurisdiction for the subsidiaries, preferably one with little or no corporation tax – such as Jersey.

The documents in the Paradise Papers show Apple was actively looking for a new home for its key subsidiaries in early 2014. The company had approached Appleby through its US lawyers, who asked Appleby’s offices in different offshore jurisdictions to fill out a questionnaire that would highlight the advantages to Apple of moving there.

In a letter from the lawyers on 20 March 2014, Appleby was asked “to provide assistance with and coordination of a multijurisdictional project involving the British Virgin Islands (BVI), Cayman, Guernsey, Isle of Man and Jersey … If your proposal is cost-effective then we will ask you to handle the entire project.”

Sixty-eight minutes later, a senior Appleby executive sent an email to other partners expressing excitement that Apple had made the approach and encouraging a swift and positive response.

“This is a tremendous opportunity for us to shine on a global basis … Please could you consider the questionnaire and provide your best fee proposal for … your jurisdiction. I … would ask that you embrace this opportunity to build a closer relationship with their prestigious client,” the email said.

The executive noted that discretion was important: “Finally, for those of you who are not aware, Apple are extremely sensitive concerning publicity and do not generally permit their external counsel to disclose that they have been engaged by Apple or to make any mention (not even generically) in promotional materials to the relevant engagement.”

Four days later, Appleby partners exchanged further emails in which they spoke of having impressed Apple’s lawyers, who had added Bermuda to its list of potential new jurisdictions – another territory where Appleby had a base.

A partner in Appleby’s Isle of Man office told colleagues: “We have tried to make our answers as attractive as possible given that we would be delighted to work with Apple.”

The need to secure a new home for Apple’s subsidiaries became urgent later in October 2014, when the Irish government made a further announcement. Delivering his budget statement, the then Irish finance minister Michael Noonan said Dublin was tightening the rules even further and would prevent companies that are incorporated in Ireland being managed and run in tax havens.

That could have jeopardised Apple’s plans for moving its subsidiaries to Jersey but for an important caveat.

Michael Noonan, the former Irish finance minister. Photograph: Bloomberg/Getty Images

Noonan said any companies incorporated in Ireland before the end of 2014 that were being run from tax havens could continue with these arrangements until 31 December 2020 – a six-year period of grace known as “the grandfathering provisions”. This gave Apple two months to finalise a move to Jersey, a crown dependency of the UK, which makes its own laws and is not subject to most EU legislation, making it a popular tax haven.

The Paradise Papers show two of Apple’s Irish subsidiaries, AOI and ASI, in the process of changing tax residency to Jersey.

Apple refused to discuss the details. But the Guardian understands ASI is now a dormant company.

Apple refused to say where the valuable economic rights once owned by ASI had been moved to but it is understood all its Irish operations are now run through companies tax resident in Ireland.

One theory is that AOE “bought” the rights owned by ASI taking advantage of an incentive called capital allowance. This means that if a multinational buys its own intellectual property through an Irish subsidiary, the cost of that purchase will generate many years of tax write-offs in Ireland.

Some experts have suggested multinationals switching intellectual property to Ireland could achieve tax rates as low as 2.5%.

Apple declined to comment on this, but said: “The changes we made did not reduce our tax payments in any country. In fact, our payments to Ireland increased significantly … (in 2014/15/16) we’ve paid $1.5bn in tax there – 7% of all corporate income taxes paid in that country.”

But Apple refuses to say how much money it makes through its Irish companies, making it difficult to assess the significance of the sum.

Apple’s financial statements indicate that it has continued to enjoy a low tax rate on its international operations. The firm made $122bn in profits outside the US during that same three-year period, on which it was taxed $6.6bn – a rate of 5.4%.

Apple said: “Under the current international tax system, profits are taxed based on where the value is created. The taxes Apple pays to countries around the world are based on that principle. The vast majority of the value in our products is indisputably created in the United States, where we do our design, development, engineering work and much more, so the majority of our taxes are owed to the US.

“When Ireland changed its tax laws in 2015, we complied by changing the residency of our Irish subsidiaries and we informed Ireland, the European commission and the United States. The changes we made did not reduce our tax payments in any country.

An Apple logo on hoarding boards outside the company’s campus in Cork, Ireland. Photograph: Bloomberg via Getty Images

It “We understand that some would like to change the tax system so multinationals’ taxes are spread differently across the countries where they operate, and we know that reasonable people can have different views about how this should work in the future.

At Apple, we follow the laws, and if the system changes we will comply. We strongly support efforts from the global community toward comprehensive international tax reform and a far simpler system, and we will continue to advocate for that.”

The company has repeatedly defended its tax affairs over the years. Its chief executive, Tim Cook, told the US Senate committee that Apple paid all the taxes it owed and complied with both “the laws and the spirit of the laws”.

The company has also condemned attempts by the European commission to get it to pay a record $14.5bn in unpaid taxes.

“The finding is wrongheaded,” Cook told the Irish broadcaster RTÉ. “It’s not true. There wasn’t a special deal between Ireland and Apple. When you’re accused of doing something that is so foreign to your values, it brings out outrage in you.”