No study based on convictions can be accurate.

Sure. That's why I used expressions like "evidence points at" and so. There simply aren't studies with representative samples of all detected and undetected child abusers... The evidence we have still points in one direction. Do you doubt that the wish to dominate, not paedophile disposition, is the motivation in the majority of the cases? If so, may I ask what reasons you have for your doubts?