Prosecutors argued that the jury who convicted him of murdering schoolgirl Jennifer Cardy had a right to know about "distasteful" material found in his van.
Black, 65, is attempting to overturn a verdict that he murdered the nine-year-old who was taken as she cycled to a friend's house in Ballinderry, Co Antrim in August 1981.
Her body, suspected of being sexually abused, was discovered nearly a week later at a dam near Hillsborough.
Black, a former delivery driver from Grangemouth in Scotland, was said to have been in Northern Ireland at the time on a work trip for a London-based poster dispatch firm.
In 2011, he was found guilty of kidnapping and murdering Jennifer and ordered to serve at least 25 years in prison.
It emerged during a six-week trial at Armagh Crown Court that he had already been convicted of killing three other girls, abducting a fourth, and attempting to snatch another.
Jurors were told how he was jailed at Newcastle Upon Tyne in 1994 for three unsolved murders from the 1980s - those of 11-year-old Susan Maxwell, from the Scottish Borders, five-year-old Caroline Hogg, from Edinburgh, and Sarah Harper, 10, from Morley, near Leeds.
Black's legal team contend that his criminal history was wrongly revealed at the trial for murdering Jennifer.
According to his lawyers, the trial should have been halted due to a lack of identification evidence against him.
But the prosecution submitted that Black's abnormal propensity for targeting pre-pubescent girls was strong evidence of his guilt.
During the trial it emerged that searches of the convicted killer's van and home uncovered tape, rags, children's clothing, child pornography and sexual objects.
He told police that he would have worn the children's clothing, including a swimsuit for a girl aged eight to ten, for his own sexual gratification.
Toby Hedworth QC, for the prosecution, argued that disclosing these details had no prejudicial effect.
The jury were entitled to know how the defendant not only dealt with a girl, but the urges he continued to have when he wasn't physically with a girl yet reliving what he had done, the barrister said.
"He had moved on to the point he was then so sexualised that he was going out looking for girls to put what had been a fantasy or interest into reality."
Appeal judges heard how striking similarities between the Jennifer Cardy case and the other three child killings is strong evidence of Black's guilt.
But defence counsel David Spens QC identified two dissimilarities - Jennifer's body was not barelegged nor had her shoes been removed.
He stressed the high threshold for admitting such bad character evidence.
Mr Spens said: "The evidence of similarities between the offences it was established he had committed before the trial and the evidence concerning the abduction and death of Jennifer Cardy should be very cogent, particularly in a case where it would constitute the only evidence of identification.
"Not only should the evidence be very cogent, it should be identical."
Following a three-day hearing the judges, Lord Chief Justice Sir Declan Morgan and Lord Justices Higgins and Girvan, reserved their decision on the appeal.
Sir Declan said: "We will give our judgment as soon as we can."