Nominet company solicitor Edward Phillips said on Monday that Cohen's company, CyberBritain Group, has formally abandoned all further attempts to get the domain it once owned back from Apple.
The battle carries some basic procedural lessons for others who find themselves embroiled in disputes over domain names.
Cohen had already lost a, at which time the judge threw the case out at the first opportunity, saying that CyberBritain could have used the appeal process that forms part of Nominet's dispute resolution procedure.
CyberBritain Group then sought a further hearing, but has now withdrawn that request and dropped the case completely, said Nominet. The company has also confirmed that it will not attempt to bring any further proceedings elsewhere.
"We always said you can't go running off to court before exhausting the process you are complaining about," said Phillips. "And a judicial review is wrong for this anyway--that is for complaining about government decisions--and we're not a government body."
Phillips added that there were many inconsistencies in Cohen's case. "Our dispute resolution procedure is designed to be very easy to use, approachable and fair. There is even an element of appeal, but he didn't use it. He said that our procedure was too expensive, but then he went off to the High Court, which is not the cheapest place in the world. He never paid a penny for the dispute procedure here."
Nominet awarded the iTunes.co.uk domain name to Apple in March this year. Apple had claimed that ownership of the domain should be transferred because it holds the iTunes trademark.
Cohen told ZDNet UK's sister site, silicon.com, in December 2004 that he had innocently registered iTunes.co.uk as part of a batch of domain names relating to music back in 2000 without any knowledge of Apple's intentions to use it as a trademark.
But the adjudicator presiding over the Nominet dispute resolution procedure, telecoms policy consultant Claire Milne,because, she said, it was an "abusive registration."
Nominet's dispute resolution policy defines abusive registration as a domain name that takes unfair advantage of a company's rights. In this case, Apple cited the fact that it had registered the iTunes trademark, together with CyberBritain's offer to sell the domain for $50,000 (?29,000) just two days after Apple offered $5,000 for it, and CyberBritain's redirection of the domain name to rival service Napster.
Cohen's response included the demand that the expert presiding over the dispute resolution procedure should not be an Apple Mac user "because in the view of the Respondent there is a 'cult' associated with the products of the Complainant, which attracts fanatical users."
Matt Loney of ZDNet UK reported from London.