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The hard drive was later examined by police, who discovered that it contained dozens of indecent images of children.
Officers were said to be 'concerned' because he was trying to access women who made no secret of having young children.
Venables is now on suicide watch in a prison's sex offenders' wing following his arrest last week.
The killer and his friend Robert Thompson were only ten when they killed two-year-old James in 1993, after abducting him from a shopping centre in Bootle, Liverpool.
Mr Bulger said that Venables, who is 35, should be given an adult life sentence for his part in the horrific murder of his two-year-old son 24 years ago.
The furious father slammed a decision to spend £5million on rehabilitation and protecting Venables' true identity and his co-killer's, Robert Thompson.'If people saw a photo of him as the adult monster he truly is they would have a very different perception of the person committing the crimes instead of a picture of so called childhood innocence,' Mr Bulger told The Sunday People.
The father of murdered toddler James Bulger is calling for an up-to-date picture of his son's killer to be shown to the world.