Frankie Robertson, 43, contacted the girl via Facebook.
He messaged her: “See when you get a minute can you send me a photo of your t**s, please?”
He asked: “Are you a model?” and said that if she sent him photographs he would pass them onto a modelling agency.
Depute fiscal Marie-Claire Chaffrey told Alloa Sheriff Court that the girl, who was 13 at the time of the incident last summer, told her mother.
Ms Chaffrey said: “The mother was extremely concerned and posted a message on Facebook asking parents to check their children’s accounts to see if they had been in contact with the accused.”
Robertson, of Alloa, was traced and arrested and interviewed at Falkirk Police Station, where he gave a “no comment” interview.
He pleaded guilty to sending the girl sexualised messages, and also admitted sending similar messages to a 15-year-old girl.
The court heard that when the 15-year-old’s mother had messaged him back telling him not to send any more messages to her daughter, he had replied with a vile remark.
Mike Lowrie, defending, said: “At the time of the messages he was in the throes of significant alcohol dependency.”
Sheriff David Mackie deferred sentence until May 14th for criminal justice social work reports, and placed Robertson on the sex offenders’ register.
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