Ranzumi

Ranzumi is the het ship between Rantaro Amami and Mahiru Koizumi from the Danganronpa fandom.

Canon
The two have never interacted in canon, since they are from two separate Danganronpa games. Mahiru being from Super Danganronpa 2: Goodbye Despair and Rantaro from Danganronpa V3: Killing Harmony. Although they never met in the official games, the two shared a seasonal event in the board mini-game Ultimate Talent Development Plan featured in the Killing Harmony bonus material that is available after finishing the game. This event is only accessible when playing through this mode with Rantaro.

Within this event, Rantaro visits Mahiru's photo exhibit during the school festival and offers her a genuine compliment, which she graciously accepts (Mahiru has famously high standards for feedback on her photography, which Rantaro meets without needing to be told). He then remarks that there is a great deal of pictures of everyone eating, to which Mahiru explains that those photos were taken at a time when Teruteru cooked food for their class. Mahiru notes that she would thank Teruteru Hanamura for the occasion if she respected him, which she doesn't, and Rantaro replies that while he does see good in Teruteru, he agrees that he's hard to defend.

Mahiru is a character with an incredibly strict moral code, and a desire to help as many people as she can. This is also notable of Rantaro, who in his killing game, went out of his way to risk his life (and even get himself killed) because he was trying to end the game and save everyone else.

Mahiru, due to a less-than-reliable father being her single parent growing up, has very high and traditional standards for the role that men are meant to play in relation to the women they interact with, claiming that men should look after and protect women. Rantaro is an individual who does all of these things to an even self-destructive extent, having lost 12 of his younger sisters around the globe, and spends most of his entire life searching for them as best he can. He even puts himself in danger often to achieve this goal.

Rantaro's real Ultimate Talent, as revealed in his Salmon Team ending, is the Ultimate Adventurer, in relation to his frequent travels. One of Mahiru's confirmed "likes", as confirmed by her student profile, is travelling.

Fanon
Ranzumi is a cross-game rarepair within the fandom. While its shipperbase is very avid and active where it exists, it's not very popular due being a cross game ship between characters with already very popular ships. Examples would be Soapies for Mahiru or Amasai for Rantaro. As of November 2021, The ship only has 10 fan fictions on AO3, though one of which is over 600,000 words featuring it as the primary pairing and Rantaro as the first-person protagonist.

This ship sailed for several reasons. Both characters express caring, "older-sibling" energies when interacting with their fellow students, both love travelling (thus opening the door for travelling together), and Rantaro exhibits all of the traits that Mahiru explicitly states that she wants men to exhibit in spades. Also, Mahiru is notably incredibly unhappy in her home life but has no way to change it, so Rantaro sweeping her away to live with him instead would make for a cute fanon dynamic. Another popular idea would be for Mahiru to accompany Rantaro on his search for his sisters, documenting their travels as a photographer.

The synergy of their talents, Ultimate Adventurer and Ultimate Photographer, should not go unremarked. Mahiru is known for enjoying smiles and photos of smiling people, and Rantaro fakes a good deal of his smiles as a defense mechanism, so a common fanon idea between these two would be that Mahiru may be able to tell when Rantaro fakes smiles.

Fandom
FAN FICTION

Amami Rantaro/Koizumi Mahiru tag on AO3

Ranzumi Sunset Beach Confession Skit on Reddit (source: u/SirMuffinsworth)

INSTAGRAM

Variations
Amachazumi refers to the ship between the two and Tenko Chabashira

Amamiozumi refers to the ship between the two and Ibuki Mioda

Amatojozumi refers to the ship between the two and Kirumi Tojo