NEW YORK » No TV for a week, the time-honored punishment for misbehaving children, has been enhanced. Now, parents are also withholding Internet access to punish their kids, further sign that the Web has become as important to families as television.

As the two mediums converge, parents are quickly coming to see TV and the Internet in similar ways and are seeking to limit their kids’ access to both, according to a report out last week from researchers at the University of Southern California.

The survey from the USC Annenberg Center for the Digital Future found that two-thirds of parents say they restrict their kids’ access to TV as punishment, a number that has barely budged in the past 10 years. But the percentage of parents who limit Internet access as a form of punishment has nearly doubled in the last decade.

Among parents surveyed this spring, 57 percent said they withheld Web access to punish their kids. That is up from 32 percent in 2000.

Michael Gilbert, a senior fellow at the center, said parents are starting to not see a big distinction between TV watching and Internet use. Even so, parents are still more comfortable with the amount of time kids spend on the Internet — 71 percent said it was "just about right" compared with just 51 percent for TV.

Earlier surveys by the center have shown that families are spending less time together than they used to, a decline that has coincided with the explosive growth of social networks in the past few years.

Now, parents are saying Internet access at home is also reducing the time their children spend with their friends face-to-face. Gilbert called this a worrisome trend, though noted that the number of parents to report this is still small — 11 percent in 2010 compared with 7 percent in 2000.

Of course, the Internet and social networks also make it easier to communicate and they help families stay in touch with loved ones.

"The answer is never about technology. It’s always about parental responsibility," Gilbert said. But he noted that the explosive growth of digital technology has made it increasingly difficult for parents to monitor what their kids are doing.

The 2010 survey was conducted in April among about 2,000 Americans over the age of 12. It has a margin of error of plus or minus 2 percentage points.