Taylor and Barton remained abroad until August 3, when they were escorted back to Liverpool by their parents and officers from Merseyside Police.
Barton had claimed he did not take a weapon with him to McGoldrick Park and he was not present when the fatal blow was struck.
While Barton was on remand at Strangeways prison in Manchester, he wrote a number of letters, which were intercepted.
The court was told: "Although the content of those letters is of no particular significance, three of those letters concluded with the same short poem, 'One, two, three, now we're trippin' on an E/We jump upon the microphone with a shout going out to Pete Daley.'"
Mr Flewitt said this was Barton bragging about the murder to his friends in code.
Taylor and Barton are expected to be sentenced tomorrow.
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