Detectives seized Craig Meehan's computer from the home he shared with Karen Matthews on Moorside Road, Dewsbury, West Yorkshire the day after Shannon went missing in February, a district judge was told.
The nine-year-old was found 24 days after she vanished.
Today, prosecutor David Holderness outlined the case against Meehan at his trial at Dewsbury Magistrate's Court.
Mr Holderness said Meehan faced charges which referred to 134 indecent images of children.
He said 133 of these were found on a second-hand computer Meehan had bought in 2006.
The other was found on Meehan's mobile phone, the prosecutor said.
He said 16 of the images have been classified as level four in a scale which runs from one to five and in which five is the most serious.
The majority of the images were classified as level one with others at level two and three.
Mr Holderness said Meehan had pointed the finger at other people who had used his password-protected computer.
The prosecutor said: "There are substantial amounts of material which, when put together, provide a convincing and overwhelming picture that it was Mr Meehan who was the person who downloaded the relevant materials."
Mr Holderness said part of the prosecution case would be matching the times at which the images were downloaded with fishmonger Meehan's work record.
Meehan, 22, denied 11 charges of possessing indecent images of children.
At the beginning of the trial today he was asked again if he continued to deny the allegations.
As the proceedings unfolded he sat in the dock flanked by two security guards sporting closely shaved hair and glasses.
He was wearing a padded sports coat over a black Manchester United away shirt.
The trial, which continues, is expected to last five days.
The court heard how police seized the computer along with another from the house in Moorside Road on February 20, initially to help them with their search for Shannon.
Mr Holderness said it was only when the machine was thoroughly examined that the indecent images were found.
The prosecutor said Meehan bought the computer from the Brighthouse store in Dewsbury in September 2006.
He said it was second-hand but the firm had wiped it clean.
Mr Holderness said extensive inquiries had taken place into the nature and thoroughness of this cleaning process but he said he was confident he could persuade the court "all of the images were not on the computer prior to the purchase by Mr Meehan".
The prosecutor said that, when interviewed by the police, Meehan did not deny the images were indecent or appear to have any disagreement over the levels of seriousness officers had classified them in.
But the court heard how Meehan did make some comment about police being sure of the ages of those featured in some of the images.
The court heard how 16 of the images were classified as level four, 11 as level three, 19 as level two and 83 as level one.
Mr Holderness told the court it was "extremely unlikely" that anyone other than Meehan was responsible for downloading the images on to the computer.
He said the images were all downloaded while Meehan was not at work.
"What the Crown would say was that the number of downloads when he's not at work make it extremely unlikely that someone else has accessed both Mr Meehan's house and his computer to carry out the downloads in question."
Mr Holderness added that two images were downloaded within 30 minutes of a file sharing program being installed on the computer.
He said it was likely that the same person was responsible for installing the software and downloading the images and that person was likely to be the owner of the computer.
Mr Holderness told the court that the image found on Meehan's mobile phone, believed to be of a 15-year-old girl, had come from his computer.
The court heard that, during police interviews, Meehan denied using the computer to access any type of pornography.
He later admitted viewing adult pornography after police found adult pornographic videos in his bedroom.
Mr Holderness said: "It was only when confronted with that evidence that Mr Meehan began to change his tune."
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