Papyrisk

Papyrisk is the friendship between Papyrus and Frisk from the Undertale fandom.

Canon
Regardless of which route the player takes, Papyrus always starts out trying to capture the human, as he hopes it will earn him his status as the official member of the Royal Guard. Depending on route, his brother Sans is trying to make him happy either by telling the human to just show up as themselves, or continue pretending to be human. When Papyrus enters the area, Sans tells the human to hide behind a conveniently-shaped lamp.

Neutral Route
While hiding behind the lamp, the human overhears of Papyrus' plans to solely capture them to stop being lonely. Upon making themselves known to Papyrus, he is very happy to see them, but he doesn't actually know what humans look like, leading to a humerous misunderstanding.

Throughout their journey through Snowdin, Papyrus continued attempts to capture the human fail either because his own puzzles are ineffectual or because Sans was too lazy to actually make a puzzle. Regardless, the human eventually makes it to Snowdin Town, the hometown of the skeletons and is given permission to comb through their house. However, should the human wish to leave town, Papyrus will be blocking the way and challenge them to a fight. However, despite acknowledging how much he wants to capture a human, the goof can't bring himself to actually kill the poor child and instead weakens them to 1 HP, then carries them to his shed to recover. Papyrus doesn't even bother to lock the door of the shed, making escape ridiculously easy, but every time the human loses to the guy, he will fill the shed with "exciting" things in order to trick them into staying.

Eventually, the human talks things out with Papyrus, allowing them entrance to Waterfall. Papyrus however asks them to hang out if they come by later. Should the human do so, they will befriend Papyrus in a parody of a dating sim, but Papyrus draws the line at them actually dating because he deems them too clingy. He still offers them his phone number and they can call at any time.

Once the player enters Waterfall, Papyrus' best friend Undyne will take it from there and try to outright murder the human to take their soul by force. Papyrus is horrified and tries to get her to ease off, but Undyne is determined to finish the job, so the human can do nothing but run from her. While they run, they get a call from Papyrus, telling them that they should try to become friends with Undyne, but only when the human hasn't killed anyone up to this point. If the human saved Undyne before going to her house, Papyrus will initiate a hang out between them, before "excusing" himself.

True Pacifist Route
Befriending Papyrus is required to unlock the best ending. He will help the human set up the relationship between Alphys and Undyne.

Then when it comes to defending the human from Asgore, Papyrus tells everyone that a "little flower" helped him rouse everyone to get them all at one place at the same time. Unfortunately, this was all a ruse from Flowey to absorb all of their souls at once, but Papyrus tells the human that he knows they can defeat him before he too is absorbed. Upon fighting Flowey's true form, the human finds Papyrus as a Lost Soul standing next to Sans. In order to get Papyrus back to his senses, the human has to remind him that they're his friend.

After everything is dealt with, Papyrus is devastated to find out that the Royal Guard has been disbanded due to capturing humans being no longer needed now that the barrier is down for good. He nonetheless cheers up when visiting the surface alongside everyone.

Fanon
Papyrisk is a popular platonic ship for both characters, with many players being endeared by Papyrus. In fact, many have abandoned a Genocide Route because they couldn't bring themselves to murder him, which is sometimes reflected in fanwork.

Fandom

 * FAN FICTION