Split and Reunion

Following

• Dragon Ball: Demon King Piccolo is a result of Kami-sama's struggle against inner evil. They live separately as foes for a time. In Dragon Ball Z, Piccolo Jr. then fuses with Kami-sama to become more powerful.
• Fate/stay night [Unlimited Blade Works]: After Archer EMIYA has been released from being Rin's Servant, he seeks to destroy Shirou with extreme prejudice because Shirou is Archer's past self. This leads to a confrontation in which, the moment their fake blades clash, EMIYA's memories are passed onto Shirou, his tragic future making him nauseous. After EMIYA explains in more detail how he came to believe that his ideals are hypocritical and futile, Shirou states that he'll never regret the path he'll choose, he'll keep saving people. This is a metaphorical merging of both of his past and future selves, only cemented by his triumph over EMIYA. With his ideals reignited, Shirou is now emotionally stabler and has gotten a few of EMIYA's moves.
• Naruto: In the Jinchuriki arc, Naruto goes to train on Island Turtle to gain control of Kurama, the nine-tailed demon he hosts. When he goes to the Falls of Truth, he comes upon a manifestation of all the trauma-induced negativity inside himself. Due to the ostracization he suffered at the hands of the Konoha villagers, all his dark feelings and hurt have festered into a dark side. Naruto must convince this side of himself to let go of the pain and accept his compassion-oriented ideals to merge into a sole personality who's healed from his trauma. This not only makes Naruto able to access Kurama's high-tier powers but also makes him better in battle as he now has a cleared mind and lighter heart.
• My Hero Academia: Inverted. Twice creates so many copies of himself through his Quirk Double that he no longer knows who is the real him. He also fears that, if he gets too injured, he'll be dispelled in the same way his clones do. After he gets rid of all his doppelgangers, he refuses to create more copies of himself and starts talking as if he has a split personality. It's only when an enemy breaks his arm and he doesn't disappear that he overcomes this fear. He then creates several copies of himself to protect Himiko from the Meta Liberation army.
• Puella Magi Madoka Magica: When Madoka makes her wish to absorb all magical girls' suffering and thus become the Law of Cycles, she ends up merging with her selves from all timelines. This means she gets their memories. It allows her to understand herself, Homura, and her friends better.

• Something Awful: Dungeons & Dragons: Subverted with Joey/Evil Joey. They never merge back into one individual.

Potter Verse

• dead things: Subverted. Harry starts as a man with a good heart and great resilience despite the trauma he's endured. After he returns from Limbo the first time, however, he slowly realizes a piece of his soul was removed alongside Voldemort's Horcrux in the process. This renders him immortal and leaves him feeling incomplete and emotionally empty. He tries his hardest for years, eventually dipping into dark magic, to reconstruct his soul. The great tragedy of the story is that he's unable to do so.
• Harry Potter And The Stolen Soul: The fic begins with a lengthy explanation of why making a Horcrux out of a living being is a terrible idea. A soul is, after all, the imprint of someone's personhood. When there's already some kind of personhood there, then you risk your soul shard getting absorbed by it. This is what happens with Harry Potter; he ends up with a second evil voice in his head advising him. The more Harry grows, the more presence his own soul becomes, so his inherent goodness becomes enough to neuter the other's malice for the most part. He gets to keep the other voice's knowledge, intuition, and cunning, though.
• The Nymph Of House Black: Since there's no issue with there being two Nymphadoras in the same timeline, even if they interact with each other, it's implied that once the toddler version grows up to 26 years old (the age at which the adult Tonks got sent back in time), the two will merge.
• Perfectly Normal: In An Abnormal Godfather, Pettigrew overhears Harry telling Neville he didn't actually destroy Riddle's diary, which prompts the rat to go looking for it in the Forbidden Forest to ingratiate himself with his master. He succeeds but ends up as the teenaged Voldemort's new meat puppet, who then goes to seek out his older self. The trope is subverted and possibly even defied because both Voldemorts are too individualistic and distrustful to work together, let alone fuse back into one soul.

Miraculous Ladybug

• Volpimania: The heroes do meet each other eventually. However, only when Volpina allows it, unfortunately, just to force them to suffer seeing the others die or already dead.

Naruto

• lie in reverse: When preteen Sasuke activated the time-traveling scroll, he split the timeline in two—one in which everything goes like in canon, and another in which his older self's presence starts changing some events. The scroll was created by the second Hokage, who didn't finish it before his death, causing, instead of the future timeline being erased, it gets layered over the current timeline. This forces the two Sasukes to fight each other for dominance until the older one loses (on purpose) and leaves his younger version with all his memories, wishes, and mistakes. This allows the preteen Sasuke to complete his arc of no longer seeking revenge against Itachi or the village, and being more appreciative of his team.

WinxVerse

• Phoenix's Secret: By the time Helia and Bloom need to return Valtor to life, she's shown being able to switch from her uncorrupted self to Dark Bloom at will—represented by her irises turning yellow and pupils becoming slits. We don't know the circumstances of how she got there, though, as the fan comic got cut short. Overall, she looks like she's stronger and more confident as a result of integrating her dark side.

• Puella Magi Madoka Magica The Movie: Rebellion: Inverted. Homura splits Madoka into two halves—her human side and her divine nature— when she comes to cleanse her Soul Gem. As pointed out both in the concept movie and Walpurgisnacht Rising, Homura thinks this is the best outcome. Madoka, the Goddess, has been forgotten by everyone she once held dear in her heart, and so is terribly lonely for all magical girls' sake. By reinserting Madoka's human side into reality, she can once again feel her family and friends' love at the cost of not being able to access her powers or remember that she used to be the Law of Cycles.

• The Dark Crystal: The Skeksis and urRa are depicted as completely opposite. From the first moments of the film, however, we can see some symmetries between them. Later they reunite and explain they were split beings. The official book about Dark Crystal world says, their split was an effect of purity pursuit.

• The Beginning After the End: During the War Arc, Arthur tends to not see eye to eye with the other Lances as they are "pretty self-absorbed and insufficient" in his own words. In particular, Bairon hates him for killing his brother Lucas. After the end of the war, the Lances are split up with Arthur finding himself marooned in the Relictombs. By the time he returns to Dicathen, the Lances are forced to fight the Asura Taci and barely survive. In the aftermath, Arthur makes up with the remaining Lances, Bairon in particular, and they resolve to be better than who they used to be. Arthur even uses his newfound insight to break the Power Limiters Kezess put on their Artifacts of Power to make them much more stronger.
• Wear Your Soul Round Your Neck: The Goddess Fountain is split into the goddess stones and the Muckpool. When Thyssa throws the former into the latter, changing it back into a Healing Spring, she feels bad for the Muckpool, but it reassures her that it's happier to be united and was proud to have created her.

• Devil May Cry 5: Due to the numerous times he lost in battle and his subsequent corruption into Nelo Angelo, Vergil is at death's door and has to split himself into two literal split personalities (V and Urizen) after impaling himself with the Yamato. In the aftermath of Mission 17, V decides to merge with Urizen again, bringing forth a re-completed Vergil who's now free from the corruption that his body suffered. He also gained new things due to the actions of his two halves; with V, it's a Character Development of interacting with Dante and Nero on a friendlier basis (which is mostly shown only after the Final Boss fight of Mission 20), while a Hand Wave from Nico's Reports imply that Vergil gained his Sin Devil Trigger form because of Urizen.
• Star Control: In the second part, the Pkunk are revealed as the offspring of Yehat, with Pkunk being New Age Retro Hippies and Yehat Proud Warrior Race Guys. At the end of the game however Pkunk visit Yehat, they are absorbed by them, and the Yehat elect a Pkunk as their queen learning from their pacifistic brothers some new spiritual insight.

• Lost in Blue: Subverted. The plot is about Cube helping Rave find his brother Cuda, as they got separated after arriving in a different world. It ends with the brothers reuniting the following day, but before Cuda can even meet Cube, she disappears.

• Avatar: The Last Airbender: In "The Crossroads of Destiny", Azula's precision lightning bending hits Aang in the back, blocking his chakras and almost killing him. This renders him unable to access the cosmic power of his Avatar State for an entire season. In "Sozin's Comet, Part 4 - Avatar Aang", Ozai accidentally fixes the issue by pushing Aang against a rock. It's in this iteration that Aang finally masters the Avatar State. He no longer feels exhausted after using it nor does he become The Berserker during it.
• Miraculous Ladybug: When Tikki and Plagg's true forms unify, they become Gimmi, the Kwami of Reality. It's unknown if they appeared before Tikki and Plagg and if so, why they split in the first place. When reunited in "Re-creation", however, they become The Omnipotent and work in perfect synchrony to grant a universe-rewriting wish to the person who summoned them.
• Steven Universe: In "Keystone Motel", Garnet splits into Ruby and Sapphire unintentionally when the two disagree on how to react to Pearl tricking them into fusing in the previous episode. Ruby is angry because fusion is so personal to them, while Sapphire (who can see the future) forces herself to remain calm because she understands Pearl's motives and knows they will eventually reconcile. Once they make up, they fuse again.
• Winx Club: When the Trix steal Bloom's Dragon's Flame, she feels incomplete and vulnerable, which might have been reinforced by how the three witches targeted her insecurities and destroyed her confidence. Some episodes later, Bloom goes to Domino and seeks her sister's advice in a frantic effort to get the Flame back. She only manages to do so by restoring her self-confidence in "The Ultimate Challenge". Her fairy transformation is stronger, allowing her to soundly defeat Icy and cast a powerful fire barrier at Alfea's entrance. Since then, nobody's been able to steal even a figment of the Dragon's Flame or block her off from it. Moreover, by the sixth season, she can even share it with her closest friends.