After looking through all the papers (and garbage cans) and going into a lot of trouble (this means torture, unwanted sex and eating spam sandwiches. I finally found out that Cartman's dad is no one else than himself.
First, aliens rarely kidnap a kid for nothing (i know that) and they did kidnapped his mother before he was born but no, no, no, they didn't give her the seeds of an unknown man. Instead of that, to be more subtile, they travelled in the future where Cartman was around 15-16 years old and kidnap him (yeah, he was born then). They took a sample of his seed and brought it back in the present where they kidnap the unpregnant mom.
Then they gave her the seed of her own future son and it worked out quite fine, she got pregnant from her own son. And this is probably a good reason why he is so, hmmmmm...Weird (but i would say socially misunderstood).
Oh yeah, you will think : But if they went into the future and he was born, this means her mom was pregnant from someone (or something) in the past?
Yeah she was but not until they came back in the past (present) to give her the seed of life, easy to understand no?
HAHAHAHAHAHAHA............