Role in South Park
Eric Cartman attends South Park Elementary as part of Mr. Garrison's class. During the show's first 58 episodes, Cartman and the other main characters are in the third grade, after which they move on to the fourth grade. He is an only child being raised by Liane Cartman, a promiscuous single mother. In "Cartman's Mom Is Still a Dirty Slut" (1998), Liane Cartman claims to be a hermaphrodite when she also claims to be the father of Cartman and that she did not know the woman who gave birth to Cartman. However, the season 14 (2010) episode "201" later reveals that Liane actually is his mother, and that his true biological father is Jack Tenorman, a fictional former player for the Denver Broncos whom Cartman arranged to be killed in the season five (2001) episode "Scott Tenorman Must Die", making Cartman and Scott Tenorman half-brothers and putting Liane's intersexual identity in question.
Among the show's main child characters, Cartman is distinguished as "the fat kid", and his obesity is a continuing subject of insults and ridicule from other characters throughout the show's run. Cartman is frequently portrayed as an antagonist or villain whose actions set in motion the events serving as the main plot of an episode. Other children and classmates are alienated by Cartman's insensitive, racist, xenophobic, anti-semitic, lazy, self-righteous behavior, but are occasionally influenced by his obtrusive, manipulative, and propagandist antics.
Kyle, who is Jewish, is often the target of Cartman's slander and anti-Semitic insults. The two have shared an enmity since the show's beginnings, and their rivalry has become significantly more pronounced as the series has progressed, with Cartman even routinely exposing Kyle to physical endangerment. Kyle has intentionally endangered Cartman as well by convincing him in "Fatbeard" to go to Somalia in hopes that he will be killed. Their rivalry stems from opposition in personalities. Where Kyle is restrained by firm morals, Cartman would rather indulge in pleasure, and goes out of his way to hurt others.
However, Kyle is sometimes an enthusiastic participant in Cartman's schemes and Cartman is sometimes seen treating Kyle well, although this is generally to put aside their hatred momentarily for a common goal, or for manipulation. Parker and Stone have compared the relationship to the one shared by Archie Bunker and Michael "Meathead" Stivic on the 1970s sitcom All in the Family. Kyle has a tendency to make what he thinks are safe bets with Cartman, and often loses these bets when the improbable actions promised by Cartman are accomplished. Cartman's motivation in this regard is not merely monetary gain, but an obsession with scoring a victory over Kyle, a fixation that ultimately plays a major part in a subplot to the three-part episode "Imaginationland" (season 11, 2007). This obsession has also proven itself to actually trump other goals Cartman wishes to achieve, for instance, in "Christian Rock Hard" Cartman makes a bet with Kyle that he can make a platinum album before Kyle can. After recruiting Butters and Token, Cartman creates a Christian rock band called Faith+1 and "writes" Christian songs by merely taking love songs and replacing words such as "baby" with "Jesus" (and which thereby humorously imply sexual relations with Jesus). Against all odds, the band becomes largely successful, managing to sell over a million copies (and potentially gain millions of dollars). However, since Christian rock bands cannot truly get a platinum album (which is not true in real life), Cartman loses the bet. Despite having amassed a large fan base as well as a large, steady income, Cartman only becomes enraged since he was unable to win a bet with Kyle. Careless in his anger accepting the Myrrh album in front of a large Christian crowd, Cartman goes into an Anti-Christian rant which drives away all of the fans as well as profits. Cartman has also been shown to have a high sadistic streak towards Kyle. He has repeatedly expressed desire in seeing him suffer. 
He has also shown to enjoy Kyle's suffering and humiliation to the extremes. 
In "You're Getting Old", the final episode of the first half of South Park's 15th season, it is suggested that Kyle and Cartman may be developing a genuine friendship, possibly due to the void left by Stan's apparent departure. This soon withers away as both return to the status quo of arch enemies at the end of "Ass Burgers", due to Kyle realizing the repulsive way Cartman was producing his burgers. Cartman's resentment of Stan is usually reserved for when Cartman proudly proclaims his hatred for both Stan and Kyle as a duo, and his contempt for Stan as an individual is usually limited to his annoyance with Stan's sensitivity, affection for animals, and relationship with Wendy Testaburger.
Despite being intolerant of other cultures, Cartman displays an aptitude for learning foreign languages. In the episode "My Future Self n' Me" when he starts "Parental Revenge Corp", he speaks Spanish to his Latino workers, though he may have learned the language in order to better exploit a labor pool. He also knows German, and once spoke a few phrases while dressed up as Adolf Hitler while promoting the extermination of Jews to an oblivious audience that did not speak German. Cartman can also be seen speaking broken German with an American accent in Season 15 Episode 2 "Funnybot". Conversely in one episode ("Major Boobage") Cartman acts as an Oskar Schindler character for the town's cats, a rare case of a subplot based on Cartman's altruism.
Cartman frequently teases Kenny for being poor, and derides Kenny's family for being on welfare. He will also use an awkward pause during a conversation as an opportunity to casually remind Kenny that he hates him. Cartman's mischievous treatment of Butters Stotch, and the relationship the duo shares has received significant focus in the more recent seasons of the series. This reflects Parker's interest; the scenes between the two are the ones he most enjoys writing.
Several episodes concern Cartman's greed and his get-rich-quick schemes, although his numerous attempts to attain wealth generally fail. His extreme disdain for hippies serves to satirize the counterculture of the 1960s and its influence in contemporary society, reflecting Parker's real-life antipathy towards hippies. Though the role is customarily taken by Stan or Kyle, Cartman will occasionally be the one to reflect on the lessons learned during the course of an episode with a speech that often begins with "You know, I've learned something today...".