Paul is a character who makes his debut in the episode Couple Skate, when Marcula sold the Aqua Teens' home a third time after the robots and the Sirens. He is a giant, muscular, terrifying monster of some kind with huge fangs, yellow eyes and four tentacle-like arms. Paul exists in a constant state of destructive, homicidal rage, which is unfortunate since he is roughly the size of a house. It is implied he has a cocaine addiction as well.
After the first two of three Marcula episodes, Carl is fed up with Marcula selling the house to more and more people, and needs to talk to him after Paul destroys Marcula's / the Aqua Teens' house in the middle of the night in a fit of rage (apparently over an ongoing child custody dispute with his ex-wife), then steals all the copper pipes to go sell for a cocaine fix. None of this bothers Marcula at all, much like the destruction the Robots rendered to the house, and his only concern seems to be forcing the Aqua Teens to pay to fix the gas leak in the living room.
After the discussion, Carl calls Frylock (who is still cocooned in the Mojave Desert with the other Aqua Teens) and plots to kill Marcula at his 4040th birthday party using a bottle of garlic champagne Frylock had been saving. Paul shows up at the party, which features roller-skating and a DJ, and after Marcula is killed the DJ makes the mistake of announcing "couples' skate", which reminds Paul of his ex-wife and prompts him to bitterly exclaim "OH BOY!!! COUPLES' SKATE!!!" and crush Carl like a soda bottle, popping his head off.
Paul reappears in Fightan Titan destroying the city (again due to his rageful nature and severe emotional problems) and the Aqua Teens must fight him in their new robot. When this fails, Frylock must placate him by inquiring about his marital problems and life difficulties, which temporarily calms the monster and keeps him from destroying any more of the city while he rants about his unfaithful wife.