Per Legal Solutions Blog you may in fact be liable for what your children do on the internet. When it comes to apps purchases, "[p]arents are accountable only for purchases by their children which they have authorized. Jeff Matsuura and Craig Blakely, Parental Liability for the Online Conduct of Their Children, Legal Solutions Blog (Thomson Reuters), available at http://blog.legalsolutions.thomsonreuters.com/law-and-techology/parental-liability-online-conduct-children/. Parents were held liable, however, in a Georgia case where parents allowed a false Facebook account to remain accessible even after the parents became aware of its existence. Id.