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1.
The Cartman Complex is simple(What'eva I'll do what I want). A person whose poor attitude has been catered to will eventually begin to believe that their attitude is acceptable. When any person attempts to impose any restriction on this attitude, no matter how small, it triggers rage in the person, causing them to act childishly until the target of their rage either bends to their will or leaves.
Naomi Campbell has Cartman Complex

Obama is a great example of Cartman Complex
by Sinschild October 27, 2010
 
2.
The un-natural obssesion with attempting to give all people who disagree with you HIV.

After the HIV is delivered the person suffering from the syndrome feels the need to crack the joke: "I'm HIV positive my way was easier", implying that they could have avoided thier misfortune simply by agreeing with the sufferer.

This term was first created after South Park Episode 1, Season 12 "Tonsil Trouble" that was first aired on March 12, 2008.
EXAMPLE:

Quote from the TV series before the event of Cartman giving Kyle AIDS, due to the Cartman Complex:

Butters: I just, eh. Well.. I don't know if I should be helping you make Kyle look silly.

Cartman: Butters. Helping People who have AIDS, is one of the most important things you could do.

Butters: I know, but are you sure Kyle has to be taught a lesson?

Cartman: I'm not just sure, butters. I'm H.I.V. Positive.

Butters: Oh yeah, eh. I guess that's true
by N1XY August 28, 2009