What's that you ask? Parental abdication of responsibility is when parents do not take and exercise the responsibility to raise their children in a manner conducive to the norms of society. Those parents seem to allow their children to be guided, or rather misguided, by whatever they see and hear and wherever they are at a given moment, with no consequence to their actions.
In an era of the two-earner family, we could blame much of this on the "latchkey" effect, where children are often left unsupervised at the end of the school day, and thus susceptible to getting into mischief or trouble due to that lack of parental supervision. However, it is interesting to note that the lack of parental responsibility is as often observed in single-earner families as in dual-earner families, so it's difficult to blame the extra effort of families who either must work to maintain a decent standard of living, or those who simply wish to "keep up with the Joneses" as being the crux of the problem with children who have a lack of parental guidance.
In the 50's and 60's, a child who was taken home by the police for a minor violation had more to fear from his parents than from the authorities. All but the most hardened juvenile would rather go to what was then known as the Juvenile Detention Center than face his father and/or mother after being brought home, as the punishment would be swift and sure. But in later years, things changed. Many children were no longer taught respect for the law in their homes, and when an officer brought a child home, they received a fusillade of abuse, rather than thanks for not taking the child to JDC. Parents started blaming the "system" for everything that their children did wrong, rather than look at what wrong their child might have done. It became the "everyone else is wrong" syndrome that pervades society today. If you doubt it exists, watch a few episodes of COPS or another similar program on television and see the response when people are caught red-handed.
Parents need to step up to the plate and teach their children right from wrong. You can't expect them to learn that from their friends who don't have parental support. Did you know that the main reason kids join gangs is because they don't have a familial unit, and the gang becomes their family? If you don't provide a family environment for them, someone else will, and it won't be loving, but it will be all they know, and they'll take to it like a duck to water.
When your children see a superstar or sports figure who has done something wrong, and been adjudicated guilty, discuss it with them. Explain that it's not a positive thing to have a negative role model. Having a rap star for a role model is cool, but not when he advocates killing police officers. Having a baseball player as a role model is cool, but not when he pumps illegal drugs in his veins. Having a football player as someone you want to aspire to be like is fine, but not when he practices cruelty to animals, and is convicted and goes to prison.
Most of all, be a parent. Being a friend is fine but first and foremost, be a parent. Your children, hopefully, will have lots of friends over their lifetime, but only one set of parents to guide and nurture them. Nobody else can take your place and if you fail at this, all the friends in the world won't help.