The trademark battle between Apple Computer and The Beatles' Apple Corps record label will likely be in a judge's hands on Wednesday.British Justice Edward Mann will decide whether to grant Apple Corps an injunction that would bar Apple Computer from using its logo related to selling music through the iTunes Music Store. The record company could then pursue damages against Apple Computer.It's the third time the two parties have met in civil court over the last 25 years, with Apple Computer paying The Beatles' caretaker company damages twice before over logo disagreements.The record label contends Apple Computer has breached a 1991 trademark agreement that prohibited the use of a bite-marked apple in connection with musical content, including the iTunes application and advertisements.The agreement, resulting from a second lawsuit, limited how the two companies could use their apples in certain fields of business. Apple Corps' label, a green Granny Smith apple, appears in the center of The Beatles' vinyl records, among other places.Apple Computer contends its logo advertises the iTunes software and services and not the musical content itself.London's High Court heard detailed testimony from two Apple executives on Monday and an expert witness for Apple Corps.Eddy Cue, vice president of iTunes, said he disagreed with Apple Corps attorney Geoffrey Vos that the logo used in the brushed silver aluminum bar in the iTunes application advertised music."I think it is used in connection with the service, not the content," Cue said.Apple Computer has submitted documents detailing how its apple disappears during the course of buying a song, complying with the agreement.Apple Corps has countered that the computer company's co-founder, Steve Jobs, has repeatedly said in public how the iTunes Music Store offers exclusive content from artists such as U2, Eminem and Bob Dylan. The label also contends the logo advertises songs not available on other download services.Whether the third lawsuit is the swan song that ends all trademark disputes between the companies is impossible to gauge.Neil Aspinall, a long-time Beatles confidant who has run Apple Corps since 1973, attended Monday's hearing and was seen speaking with Apple Computer officials after the day's testimony.Aspinall's affidavit sheds light on relations between the iconic companies. The 13-page document, dated March 1, says Aspinall was told by Jobs that he named the computer company after the record label.In March 2003, Jobs offered $1 million for the rights to the name Apple Records, according to Aspinall."I rejected this offer," Aspinall said in the document. "I did not expect that Apple Computer would attempt to use the name 'Apple' and apple marks in connection with prerecorded music."