question about illegal downloading

Sorry for being dumb and I'm no computer or law expert, the question is:

If I download music or movie illegally or perhaps CP,ok? If everything I downloaded was free(i.e. no credit card record) then even if the police can seize my computer, in my home, how could they prove me did it but not my father or mother or my brothers if every one in my family can access the same computer?
They can't just sue every member of my family, right?

If there ever is such a problem, the owner of the PC gets in trouble unless there's proof otherwise.

So in your case, your father would probably be the one responsible, unless it's obvious the files in question are on your user account / only accessed by you / etc.