I think I liked it better when you weren't around...
It is true that the Absent Parents might be assholes for leaving their kid(s) to fend for themselves. However, there are also cases where the parents are still around and their assholishness stays with them. Enter the Deadbeat Parents. These people apparently didn't have a good plan for having children, and while some might evolve later on and rise above, others continue to mooch off their children and whatever other source of income they can find, slack off and get drunk, or otherwise force the kid to be more mature than the mom and/or dad who supposedly gave birth to them.
Example: Michiko Malandro kept watch over her daughter Hatchin, but only because she thought she could lead her to Hiroshi. While Michiko was the one getting drunk and pissed off in her search, Hatchin was usually the one taking jobs and earning money while trying to keep her mother on the right path.
Another example: in Hayate the Combat Butler, Hayate's parents are never actually seen, but even at the very beginning they steal what little money their son has, gamble it all away, and then sell him to the Yakuza to pay off their own gambling debt, the same one that hangs above his head throughout the entire series.