This isn't settled yet, but an intermediate appeal court in Georgia has held that parents could be liable for the misdeeds of their kids who create fake FB profiles that defame other kids:
The Georgia Court of Appeals ruled that the parents of a seventh-grade student may be negligent for failing to get their son to delete a fake Facebook profile that allegedly defamed a female classmate.
The trouble started in 2011 when, with the help of another student, the boy constructed a Facebook profile pretending to be the girl. He used a “Fat Face” app to make her look obese and posted profane and sexually explicit comments on the page depicting her as racist and promiscuous, according to court documents.
When the girl found out about it, she told her parents who then complained to the school’s principal. The school punished the boy with two days of in-school suspension and alerted his parents, who grounded him for a week.
...
The parents intend to appeal to the Georgia Supreme Court. So this may be a while.
