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Ricky manages to make Karl laugh at one point in the show. The heartwarming part comes from how happy Steve and Ricky sound to hear Karl actually laughing.
One of the most uncomfortable episodes of the old XFM show is the one where Ricky and Stephen pressure Karl into doing silly record breaking attempts, and Ricky shouts at him when he fails. But in the next episode, Karl has apparently told them that they've gone too far, and the three have had a serious conversation. They have come to some new agreements, including Ricky no longer being allowed to squeeze Karl's head anytime he likes. It's one of the few moments in the original show where Ricky and Stephen treat Karl with respect and openly show that they value his friendship.
Someone once asked Karl who he would choose between Ricky and Steve if a boat was sinking and he only had time to rescue one. Karl couldn't choose between the two.
An EXTREMELY subtle one occurs in the old XFM shows. Karl tries to crack a joke about Steve by calling him an "invalid", which greatly upsets Steve. One would expect Ricky to make a snarky joke of sorts at the others' expense. Instead, he is silent for a few moments before quickly changing the subject and playing a song someone had requested them to play. In other words, he figured Steve was dealt a low enough blow that insulting him furtherwould be too cruel.
Karl buys Ricky and Steve Christmas presents. This from a man who brought his girlfriend a box of condoms and Grease.
Basically anytime Karl, Ricky and Steve all get along. To paraphrase Ricky, 'It's like we get him at the weekend and we let him eat all the sweets he likes.'
The finale of the animated series is an odd combination of heartwarming, funny, and maybe a little tearjerking. After one of Karl's usual rants on everyday life, this time about how insistent people are on turning lights off and conserving energy, Ricky bursts into laughter and exclaims how he can't wait for Karl to be old, and for the three of them to all be in a little home together. The three are shown in their old age, Ricky still laughing, as a big orchestra score plays and the camera zooms out of the window of their little home, and into the sky. The moment still remains a bit heartwarming even as Ricky exclaims "What a fucking useless bunch of cunts!"