If Toriel, Undyne, and Mettaton are all dead, then Papyrus becomes King by process of elimination, but his brother Sans does all the actual work. If Undyne becomes ruler because Toriel is dead, then she appoints Papyrus to 'The Most Important Royal Position', which consists of sitting around and looking cute.

If Toriel becomes Queen and isn't overthrown, then she makes Papyrus 'Captain of the Royal Guard', with his only duty being to tend the castle garden.

Authority in Name Only: Some of the Neutral Endings involve this.

Defeating him at the edge of Snowdin marks the end of the first portion of the game, and begins the Waterfall section. The player must make their way through the traps that Papyrus sets in the forest on their way to Snowdin, with information about Papyrus and his motivations (his loyalty to Undyne and his desire for respect and friendship) being revealed along the way. Papyrus wants to capture the main character because he wants recognition, respect, and love, will hurt but won't kill, and has no problems with stopping being 'evil' if you choose to befriend and spare him which is exactly what he wants. Sans is amused at Papyrus being so Endearingly Dorky and Papyrus has this reaction towards his older brother being lazy. Calling him at one point in Hotland will have him insist that anime is for children, an observation that annoys Undyne, of all people, who thinks anime is real. Despite his childish demeanor, Papyrus seems to be a believer of this trope. He almost always sounds irritated and fed up when talking to you about Sans, but it's pretty obvious that most of it comes from the fact that he's concerned about his well-being, and his terrible jokes, of course. Though there's not much evidence from Papyrus specifically, he qualifies by association due to them being (presumably blood-related) brothers.

Ambiguous Disorder: Papyrus has No Indoor Voice, is a bit socially unskilled, to the point he needs a guide book when he's on a date, and interprets insults towards him as compliments or self-insults, shows strong interest in puzzles and cooking spaghetti, as well as having a few 'childish' behaviors like collecting action figures, having a race car bed and needing a bedtime story and despite coming across as ditzy, immature and naive, he is a surprisingly skilled fighter and is implied to know more than meets the eye.

On his Twitter, Toby Fox has stated that Papyrus doesn't really get concepts like relationships and sex, a notion that's very much supported in the game, so speculating on his sexuality is likely a wild goose chase.

All in all (especially since this is Papyrus we're talking about), it's hard to tell. He's very close to Undyne, but ( obvious issues aside) there's nothing to indicate they're anything but Platonic Life-Partners, and he has optional dialogue in which he calls Mettaton 'his favorite sexy rectangle', which very well could be just an objective observation more than anything else.

He's willing to go on a date with the protagonist, who is of Ambiguous Gender, if they flirt with him, but apologetically 'dumps' them right afterward, saying that he only did it because he felt obligated to and only ever liked them as a friend.

In one phone call, Undyne addresses Papyrus by his name, and he asserts that he is actually CoolSkeleton95, his Undernet persona.

Alter-Ego Acting: In-Universe, and a very minor case.

He persists in this belief even after dying in such a run. In fact, he'll spare a No Mercy run protagonist on the spot just because he believes they have some good in them.

All-Loving Hero: Heroic in the sense of always trying to do good (even if he's a bit of a goof and a lot of a Cloud Cuckoolander), and unrivalled in compassion and friendliness.It's implied that he's trying to appear too cool for lame jokes and hates it when Sans catches him smiling. Actually Pretty Funny: Despite having regular Lame Pun Reactions, he usually has to keep himself from laughing at them and he himself cracks a few puns here and there.and by that i mean he wears it in the shower.

Papyrus fight