The New York Times has a good discussion of the Kaiser M2 Report about kids and (multi) media. “As parents, we’ve spent nearly 50 years trying to keep children away from media, and look where they are now: swimming in it.”
Some of the highlights include:

As concerned parents, perhaps the best we can do is to carve out time for our children to experience the old ways — of communicating, playing and sharing information — as well as the new. Psychology professor Georgene Troseth, who advocates delaying the introduction of media to younger kids and imposing restrictions on older ones

Yet many parents are telling me that modern media acts like a drug because their child now has an addictive relationship to small and larger screens. They seem to act as a comfort blanket for older kids who can certainly “lose it” like a toddler if their social prop gets lost or confiscated for misuse. I would therefore say parents are being shortsighted and possibly selfish, rather than negligent in allowing children apparently unfettered access. Negligent means willfully ignoring the obvious, which isn’t yet there. Child development specialist and author of a book on encouraging childhood friendships Elizabeth Hartley-Brewer

Media are arguably children’s leading educator about the world and about how they should behave in it. The question we have to ask now is what, exactly, they’re learning. Michael Rich of the Center on Media and Child Health

I have also found that this consumption of media was predictive of psychological and behavioral problems, after accounting for parent and child characteristics and poor eating habits. What’s more, parenting style was directly related to healthy online behavior: Parents who set clear limits and boundaries but did so with warmth and consultation with their children, had children who were less consumed with media, possessed higher self-esteem, were less depressed and had better relationships with their parents. Psychology professor Larry Rosen