The European Commission has published enormous detail in its final report on Apple.
It reveals the structures which allowed the tech giant pay minuscule amounts of tax.
The company has two subsidiaries, Apple Operations Europe (AOE) and Apple Sales International (ASI), which have no physical presence and no employees.
One of the subsidiaries, ASI, had profits of $25 billion in 2014, but it paid less than $10m in tax.
The commission's report outlines the evidence for its ruling that Apple must pay €13bn in tax in Ireland.
It also details how the Irish Revenue Commissioners agreed with the company's tax proposals.
The European Commission said that agreement constituted State aid.
It said: "Ireland had not put forward any justification at all for the selective treatment" of Apple.
The Department of Finance denied that Ireland provided any favourable tax treatment.
It accused the commission of misunderstanding Irish law and of wrongly interpreting its own rules.
Apple said the latest report from Brussels had ignored the opinions of Irish tax advisors.
The American Chamber of Commerce in Ireland has backed the Government's position to appeal the tax ruling. That case will be heard in the European Court of Justice.
It is there the final decision on this controversial judgment will be played out.
At the end of August the European Commission published its long-awaited findings into whether or not the Government had broken European state aid rules by granting Apple two special tax deals in 1991 and 2007.
The commission's conclusion stunned the Government: it said Apple had been granted a benefit of €13bn by the Irish tax authorities, money the company would have to repay.
The decision drew a furious reaction from Dublin, and it posed an immediate challenge to the minority Coalition over whether the Government should appeal the decision.
Some Opposition TDs said the €13bn in alleged tax arrears could be spent on vital public services.
The publication of the full report today was delayed so that sensitive commercial information relating to Apple could be redacted.
It is understood that since 1999 the commission has adopted hundreds of state aid decisions, with tax being recovered in 150 cases.
This is the biggest amount ordered to be recovered ever but was a normal case in terms of procedural aspects.
The investigation showed Apple received a very favourable ruling in Ireland and received a special deal.
Apple launches legal challenge
Apple has hit out at the European Commission, and launched a legal challenge overnight.
In a statement, Apple said it was confident the ruling would be reversed.
It said: "It's been clear since the start of this case there was a pre-determined outcome.
"The commission took unilateral action and retroactively changed the rules, disregarding decades of Irish tax law, US tax law, as well as global consensus on tax policy, that everyone has relied on.
"If their opinion is allowed to stand, Apple would pay 40% of all the corporate income tax collected in Ireland, which is unprecedented and, far from levelling the playing field, selectively targets Apple.
"This has no basis in fact or law and we're confident the ruling will be overturned."
Apple stressed that it has paid billions of dollars in taxes and created 1.5 million jobs across the European Union.
In its legal arguments published today, the Department of Finance said: "The commission has exceeded its powers and interfered with national tax sovereignty.
"The commission has no competence, under state aid rules, unilaterally to substitute its own view of the geographic scope and extent of the member state's tax jurisdiction for those of the member state itself.
It added: "The commission never clearly explained its state aid theory during the investigation, and the decision contains factual findings on which Ireland never had the chance to comment.
"The commission breached the duty of good administration by failing to act impartially and in accordance with its duty of care."
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