(CNN) -- It probably won't surprise you that millions of underage kids -- some as young as age 8 -- are on Facebook, despite rules that prohibit children under 13 from joining the social-networking site.
What may be more startling, however, is this: Their parents are helping to sign them up.
These are among the findings of a new study appearing this week in First Monday, a peer-reviewed online journal. The four co-authors of the study argue that such age restrictions, inspired by the Children's Online Privacy Protection Act, or COPPA, are mostly ignored by kids and parents and only encourage dishonesty.
"Our data show that many parents knowingly allow their children to lie about their age -- in fact, often help them to do so -- in order to gain access to age-restricted sites," the authors wrote in the study's introduction.
The vast majority (95%) of the parents of 10-year-olds on Facebook were aware when their child signed up for the site, and 78% of those parents helped create the child's account, according to the study. For 11- and 12-year-olds, the percentages of parental knowledge and involvement were slightly lower.
Although 89% of the parents surveyed believe there should be a minimum age for Facebook, 78% believe there are circumstances that make it OK for their child to sign up for an online service even if he or she does not meet the site's minimum age requirement.
When asked what these circumstances might be, parents most often cited school-related activities and communicating with other family members.
The study is based on a July survey of 1,007 parents in the U.S. who had kids ages 10-14 living with them. According to its findings 55% of 12-year-olds and 32% of 11-year-olds were on Facebook, while 19% of 10-year-olds were active on the site.
The question of what age is appropriate for kids to join social-networking sites has been debated by privacy advocates and parental groups for years. Facebook CEO Mark Zuckerberg himself has said that children younger than 13 should be allowed on his service because interacting online is an important part of today's educational process.
A study by Consumer Reports last spring found that 7.5 million children under 13 are members of Facebook.
Legislators enacted the COPPA law in 1998 -- the early days of the modern Internet -- to protect kids against predatory marketing, safety risks and other abuses that may result from others having access to their other private data. COPPA requires websites to gain "verifiable parental consent" before collecting information on children under 13.
But many sites, wary of the headaches involved with trying to enforce the law, simply added age restrictions to their terms of service -- those wordy legal documents that users rarely read before signing up.
The authors of the new study argue that COPPA has had unintended consequences -- restricting kids' access to the Internet while encouraging parents to act unethically -- and suggest that the age-based law should be replaced by universal privacy protections.