Dad Simon

Simoline is the family ship between Simon Petrikov and Marceline Abadeer from the Adventure Time fandom.

Season 3
Hints that Marceline and the Ice King know each other are dropped when Marceline joins Finn and Jake and a few others watching the Ice King's old tapes in "Holly Jolly Secrets".

Season 4
After a some foreshadowing, the episode "I Remember You" confirms that the Ice King is familiar with Marceline, covering one of her songs to Gunther. Believing that writing and performing a song to Princess Bubblegum will lead to her falling for him, the Ice King gets the idea to collaborate with Marceline for it. Needing material, he goes through old documents and letters he had never sent, intending to use these as lyrics.

Finn and Jake catch him trying to enter Marceline's home and think he's trying to harass her, but Marceline gently tells them to back off and lets Ice King inside. She seems to be okay with them spying outside her house should anything happen. When Ice King tells her that he wants her to write a song with him, Marceline seems confused and disappointed, also irritated that the Ice King "found" her. She nonetheless sits herself down on her keyboard, letting him improvise a song about how much he loves Princess Bubblegum. The subject matter already made her uncomfortable, along with the Ice King talking himself up to her. But then she notices that the song meets a swift end when the Ice King starts breaking down over the thought of being alone forever and not knowing why. This causes his ice magic to act up, freezing parts of her living room solid. Marceline gets fed up with him and tells him to stop "acting crazy", but the Ice King pushes her and immediately regrets it.

Apologetic over it, the Ice King scurries to the top of Marceline's fridge and continues to bother her when she's tired and trying to get a snack. The drops the apple she got from the fridge, rolling it towards her keyboard and letting the song it recorded play out while improvising a new song about the Ice King. In it, she laments how annoying he is, despite how much she's trying to help him. She also reveals that this is not the first time the Ice King sought her out, believing the song to just be another excuse to see her. When she admits that Marceline is actually glad to see him, the Ice King is in disbelief over her actually liking him and offers her a hug. Smiling for the first time that day, Marceline accepts it, only for her to push him away when he tries to kiss her. Telling him that he should've known that she doesn't like him that way, she calls him "Simon".

When the Ice King doesn't recognize the name, Marceline desperately tries to make him remember. Among the scraps of documents he brought with him, she finds a photo of herself as a kid, telling him that she remembers him taking it. When she notices sentences written on the back of the photo, the Ice King drags her to the instruments in the room, believing them to be potential lyrics. Marceline sings them, revealing they are actually a poem Simon left for her before the crown took his sanity along with his memories. Marceline only grows more desperate and gives Simon another note he wrote to her, but he just sings it without thinking or remembering. Eventually, Marceline gives up and grabs her bass, moved to tears over the thought that her father figure doesn't remember her. But she remembers how Simon found her before the crown drove him mad, she was crying and all by herself. To cheer her up, he took a teddy bear from an abandoned toy store, Marceline loved that bear, "Hambo", and it became her favorite toy well into adulthood.

Fanon
Many credit the backstory behind Marceline and the Ice King on fan enthusiasm, as people speculated that they had a connection due to being the oldest characters in the cast long before it was confirmed. "I Remember You" became remembered as the episode that showed the true potential of the series in telling emotionally moving and heart-wrenching stories, forever changing the show's reputation for the better.

As a result, Simoline continues to be the most popular platonic ship, even overshadowing FinnJake, despite them being the main characters.

Fandom

 * FAN FICTION