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Death Note fanfiction not only has its two overwhelmingly popular pairings of L/Light and Matt/Mello, but also predictable storylines of just how they get together. L and Light frequently fall in love during the Yotsuba arc, often with special attention paid to the anime-only rooftop rain scene and averting the canon outcome of the 13-day test.
Matt/Mello fanfics often include a teen romance (perhaps unconsummated) in Wammy's House, Matt's heartbreak over Mello leaving to join the Mafia, and then later include angst over either Matt's death, Mello's death, both, or if their canon fates are avoided, their near-brushes with death. If the fanfic is non-angsty, Matt/Mello often appears as a secondary couple in a Ship Mates fanfic along with L/Light, with all four working as detectives together and getting along surprisingly well, despite Light being a (possibly reformed) serial killer.
The most common type of Death Note fic is Light and L's kinky chain adventures during the Yotsuba arc.
Light complains about L eating so much sugar and not letting him sleep. L complains about the time Light spends on personal hygiene.
Light and L forget that they are working on a high profile murder case and are paranoid neurotics and go to the movies / beach / mall / candy store / fun place for no good reason.
Light forgets that he's on a righteous crusade to eliminate evil and because of the power of twu lub gives up the notebook to be with L.
Mr. Yagami gets mad at L or Light for sleeping together.
Sometimes L/Light and Matsuda/Sayu are Ship Mates which leads to much banter and teasing.
Light gets raped and L comforts him.
L gets raped or just hurt/traumatized by Beyond Birthday and Light kills Beyond and comforts L....
...OR L gets raped or just hurt/traumatized by Light and Beyond kills Light and comforts L.
Misa is a hateful bitch and tries to kill L and/or Light.
For the rare het fic: Misa is a stupid puppet that does whatever Light tells her.
Light is an abusive ass, Misa falls in love with L, and Misa or more commonly Rem cuts a deal with L.
Mello gets into a fight with Matt about lack of chocolate or ignoring him in favor of his video games.
Beyond Birthday arrives to rape/dismember/kill L, Light, Mello, Near or whatever Woobie of choice.
Light becomes a Shinigami.
Light develops Dissociative Identity Disorder.
Rewrite the show so that Light never picked up the notebook.
- Another character picked up the notebook instead...
L's Back Story is finally revealed. It's very dark and tragic.
Light's Back Story is examined and he's often given a Freudian Excuse.
Ghost Shipping with L.
Matt saves the day.
Mello lied about having no interest in Sayu. Sayu is raped by the mafia guys. Or Mello saves her to rape her himself.
A Mary Sue with a tragic past falls into the Death Note world from our world and derails the plot with her charms.
A Mary Sue with a tragic past arrives at Wammy's House but eventually gets kicked out for being smarter than everyone else and goes on to pair up with the character of choice.
A Mary Sue with a tragic past has a super special Life Note and the Eyes and a Shinigami buddy at her side and goes on to pair up with the character of choice.
Then there's the High School AU of course where L and the Wammy's kids are a big happy family and the Kiras are troubled, outcast Emo kids.
- Just as often it's a College AU where the cast goes to college together.
Matt and Mello (sometimes with Near, L, and Light) do teenager-y stuff.
As the psychological warfare continues to escalate the characters challenge each other to a game of Truth or Dare or Spin the Bottle or Strip Poker.
L spontaneously gives the taskforce a day off to get some alone time with Light.
L watches Light have A Date with Rosie Palms on the security cameras.
For Continuation Fic Matsuda is either a) very guilty about shooting Light, b) becomes the next Kira, c) hooks up with Sayu or d) all of the above.
The Next Gen Fic starring an OC that is Light and Misa's kid. Expect L to have a kid too and Generation Xerox of most of the characters.
Expect fics about unwritten rules of the notebook such as, say, enabling men to get pregnant.
A character is brought back to life with the death eraser.
Peggy Sue is common with plot points going much the same way as canon despite a character's forknowledge of events.
Mello and Near (sometimes with Matt and Linda) work together against Kira.
Mikami becomes Light's insane stalker and someone, usually L, has to save him.
For the epilogue Misa is easily talked out of killing herself so that shipping may commence—usually with Matsuda or Sayu.
Mikami carried a backup page for the final confrontation.
Light comforts poor little orphan B and L and Watari are evil bastards abusing and experimenting on children.
Have characters meet earlier on and develop friendly relations and so derail the The Stations of the Canon.
A crossover character (and/or Possession Sue) derails the plot.
L and Light team-up against an eviler, incredibly brutal OC Kira. The OC will often be 1) so brutal in his/her methods that it makes Light ill to show how much more eviler s/he is 2) a graduate of Wammy's House.
Assassin and mafia AUs are common.
Light stupidly gloats giving away his plans so L catches him easily and hooks up with Misa or an OC.
For Continuation Fic Sayu discovers where her brother hid the real notebook becomes the next Kira and avenges him.
A Mary Sue just happens to recognize L and instead of getting freaked out about it (as L would in character) sex ensues. The same formula goes for a Mary Sue with Kira.
The AU where Misa is doing her modeling work and L becomes her creepy boss.
- The AU where Light is a male model and L is his creepy boss.
One or more characters is actually a sexy vampire. Or a sexy werewolf. Or a sexy whatever. The important part is that they can't be killed with the Death Note and sex ensues.
The AU where the Yagami family lost all their money so Light has to go work for the wealthy Lawliet family in order to support his little sister...