Some two-thirds of American parents monitor their children's Facebook activities, but a large percentage say they trust their youngsters to manage on their own, a study showed Thursday.

The survey by the Annenberg Center for the Digital Future at the University of Southern California found 70 percent of parents keep tabs on their kids' Facebook accounts. Some 46 percent had passwords.

Yet 30 percent said they allow their children to manage their own social media activities, with some saying it was because they trust their children, or because monitoring would indicate a lack of trust.

Nine percent of those who allow children to roam free on Facebook said they did not know how to use the social network, and seven percent said they lacked time.

"It's every parent's dilemma to know when to trust their children," said Jeffrey Cole, director of the center.

"In the last five years, we have seen many new issues about parenting and technology evolve that previous generations never encountered.

"How parents cope with their children using social media like Facebook represents only one aspect of these issues."

The survey also asked adults at what age the children in their households should have a mobile phone or Facebook account. They responded the appropriate average is 13 for mobile phones and 15 for a Facebook account.

The findings are part of the 2013 Digital Future Project, the longest study of its kind of the views and behavior of Internet users and non-users.