I don't know how far this question intends on taking 'blame.' If the question refers to jail time or other criminal justice involvement, I would say that they should not be held responsible. If the child damaged property or caused injury, the parents should be economically liable. I would also consider parents being forced into counseling or classes that may help them reduce their child's violent tendencies.
I think that a parent is resonsible for the actions that their child takes, any agressive actions taken by the child should be blamed on the parents since the parents should have had more oversight and control over their child, I think that holding parents accountable is a good thing.
There are plenty of conduct disorders carried within children that affect the way they behave and the way they show their emotions. This can result in them becoming a offender at a young age. Maintaining and helping the child takes work and talking about working, it might not even have an effect!
Parents should not be blamed for their children's aggressive actions. Children are capable of making their own decisions and it would be unfair to put excessive blame on a parent for their children's aggressive actions. Unless the parent raises their child in a manner to effect their aggressive behavior, parents are not responsible for every thing their children do. Parents must do the best to raise their kids so the behave properly in social settings, but every action that a child makes is not in the control of the parent.
Peoples attitudes are pretty much set from the time they are born. They are born with certain chemical make ups in their brain that makes them aggressive. So in some ways the parents are to blame because they supply the genes for the kid. But in reality it is basically a chance kind of thing and shouldn't be put on parents too much.