Cartman's Mom is a Dirty Slut

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South Park Season 1 - Episode 113 - Cartman's Mom is a Dirty Slut
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South Park Episode 113 - Cartman's Mom Is a Dirty Slut
This South Park episode was originally aired on 25th February 1998.
Cartman has been absent for school for some time, and the boys go to his house to find out what's wrong. Cartman has become depressed about not having a father. Cartman confronts his Mother about it, and she says that he was conceived at the 12th Annual Drunken Barn Dance. Meanwhile, Kyle and Stan enter a videotape they made of Cartman holding a tea party with stuffed animals in the weekly contest held by America’s Stupidest Home Videos.
Cartman's mom is named Liane after Trey Parker's former fiancée. He caught her with another man once, and he now names every easy female character after her.

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(The complete plot for this South Park Episode)

Stan, Kyle and Kenny decide to check on Cartman when he does not show up for school. They discover that he is having a "tea party" with his stuffed animals in his backyard. Their school counselor Mr. Mackey advices them to videotape Cartman, so he can study him psychologically. Meanwhile, Cartman does not have a father to take to the annual father-and-son dance and asks his mother who he is. His mother explains that she met his father, a Native American named Chief Running Water, at the 12th annual "Drunken Barn Dance". However, Chief Running Water informs him that his mother dumped him for Chef. Chef tells Cartman that his mother preferred Mr. Garrison over him. Mr. Garrison admits that he had slept with Mrs. Cartman, but then argues "But who here didn't!?", to which Mayor McDaniels, Principal Victoria, Jesus and Father Maxi share guilty glances with each other. Dr. Mephisto is willing to perform DNA testing to resolve the issue, but requires $3,000 for the test. Cartman gets depressed, as he does not have the money.
In the meantime, Kyle, Stan and Kenny watch America's Stupidest Home Videos, they hear there's a $10,000 grand prize for the stupidest home video. They decide to enter the competition with the video they made of Cartman. Cartman approaches Kyle and Stan while Kenny was dragged to a train track by Stan's Go-cart and is run over by an oncoming train, with the depressing news about his lack of funds to find out his real father. Stan and Kyle agree that if they win the video contest they will give Cartman the $3,000 needed for the DNA testing. Cartman is overjoyed, but quickly becomes extremely angry after seeing the aired video. Though they do not win the competition, as Stan's grandfather wins with a videotape he made of Kenny's death, they receive a $3,000 runner-up prize instead, which is still enough for the DNA test. Dr. Mephesto calls together Cartman, his mother and all potential fathers, including the 1989 Denver Broncos, when he gets the test results which is where Kenny comes back to life. When he is about to reveal the identity of Cartman's father, a narrator states that the answer will be revealed in the new South Park episode four weeks later, much to Cartman's annoyance.