"H'El on Earth" is a Superman crossover story arc published by DC Comics in Superman Vol. 3 #13-17, Superboy Vol. 6 #14-17, Superboy Annual #1, and Supergirl Vol. 6 #14-17 from October 2012 to February 2013.
The story begins as Kon-El, a telekinetic genetically-engineered to mimic the powers of Superboy, H'El. H'El claims to be a Kryptonian. Clones were outlawed on Krypton, and H'El believes Superboy to be an abomination. H'El easily outmatches Superboy and teleports away with him. H'El later kidnaps Supergirl while she sleeps, taking her to the Sun. He shows her the unconscious body of Superboy, and explains that he was sent to Earth by her Jor-El before the destruction of Krypton. He says he has a plan to save Krypton, and shows her the unconscious body of Superboy (which she also believes is an abomination). Supergirl introduces H'El to Superman. H'El tries to kill Superboy, but Superman stops him. Superboy wakes, and he and Supergirl attempt to intervene. H'El critically injures Superboy and knocks Supergirl out. He implants a telepathic illusion in Supergirl's mind, making it appear as if Superman attacked her.
Superman brings Superboy to the Fortress of Solitude, where he places the teenager in Kryptonian battle armor to keep him alive. H'El and Supergirl appear, and Superman flees the Fortress with Superboy to save Superboy's life. Supergirl enters the Bottle City of Kandor and retrieves a crystal. Suspecting H'El is not a natural Kryptonian, Superman talks to Lex Luthor (who bioengineered Superboy). Luthor argues that the only way to save Krypton is to go back in time. To do so, H'El will need a Kryptonian crystal and the entire energy of the Sun. H'El will destroy the Solar System to save Krypton, and Luthor mocks Superman by saying that he will have to kill H'El to do so.
With the Justice League's help, Superman tries to stop H'El. He traps Superman using an alien imprisonment device that shunts the Man of Steel into a parallel dimension. Superboy saves him, but by the time they return H'El has already activated his time machine. H'el takes the armor off Superboy and battles Superman. Wonder Woman uses he magic lasso to force Supergirl to see how H'El has lied to her. H'El disappears into the past. A dying Superboy destroys the machine, saving the Earth. Superman saves Superboy by replacing the armor.
In an epilogue, a young Jor-El finds an injured H'El in a cave deep below Krypton's surface.
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A year later, from October to November 2013, the "H'El on Earth" story is concluded in "Krypton Returns". That was another crossover story that occurred in Action Comics Annual #2, Superman Vol. 3 #23.3, Superman Vol. 3 #25, Superboy Vol. 6 #25, and Supergirl Vol. 6 #25.
H'El is in a coma, and Jor-El had been running experiments on him to determine what kind of creature he is (since he is obviously not a pure Kryptonian). H'El's telepathic mind is awake, however, and he listens in as Jor-El tells his friend, Zod, about his plan to collect genetic material from through Kryptonian history and launch it in a spacecraft to Earth. H'El realizes he is a product of this genetic material. He wakes, kills Jor-El and Zod, and launches the ship (ensuring his own creation).
Superman, Supergirl, and Superboy (Kon-El) arrive at Krypton's location in the present-day. They discover H'El has saved the planet and enslaved the population. Massive temporal disruptions pulse through space, and Superman realizes H'El has traveled through time repeatedly to save the planet from destruction. These temporal distortions threaten to destroy the universe. They decide to travel to different points in time to stop H'El: Supergirl travels deep into Krypton's past to prevent the clone rebellion from damaging Krypton. Superman travels to Kryptonopolis the month Krypton's destruction to stop H'El when he first arrives. Superboy travels to Argo City a week before Krypton's destruction to make sure Kara escapes to Earth.
The Great War (also known as the Clone War) occurred 100,000 years in Krypton's past. For 10 millennia, Kryptonians had used cloning technology to make themselves immortal. When an alien known as The Cleric arrived on Krypton, he sparked a debate as to whether clones had rights. This ignited a thousand-year-war, during which Krypton was turned from a lush paradise into a blasted ruin of a world, the population living in isolated citadels of high-technology. One "purist", Kem-L, steals The Cleric's "Eradicator" (a device intended to keep the Cleric alive by purging damaged DNA from his aging body) after a large group of Kryptonians announced their decision to leave the planet. He changes their DNA so they become allergic to the common element lead (inadvertently creating the Daxamite race). Realizing this is not enough to stop further emigration, Kem-L uses the Eradicator to alter the DNA of all Kryptonians -- causing them to die if they leave their homeworld. Although The Cleric regains control of his Eradicator and leaves Krypton, the damage done to Kryptonian DNA cannot be reversed. During the Great War, a pro-clone rights group creates an atomic gun to destroy Krypton. Although the "Destroyer" is turned off and everyone thinks the planet is safe, in fact the process has only been slowed down. (This is why Krypton explodes at the time of Jor-El.)
Supergirl realizes that H'El changes history by defeating the pro-clone rights rebels. This prevents them from creating the Destroyer. When Supergirl arrives at the Great War, her anti-clone bias leads a battalion of clones to attack her. She defeats them but is seriously weakened. She encounters H'El and they fight. The clones, realizing Supergirl is attacking their enemy, help her. H'El is defeated, and commits suicide once he realizes he has not saved Krypton. Supergirl returns to the present.
Arriving at Argo City, Superboy meets Kara Zor-L. He's attacked by the Eradicator, which has returned to Krypton. The Eradicator, somewhat sentient, has come to see Kryptonians as biologically impaired and now wants to ensure that all Kryptonians die when the planet explodes. Superboy defeats the Eradicator, but is distracted by the arrival of Superman's mother, Lara. The Eradicator attacks again, and Superboy uses a warp conduit to shunt it onto Earth into the present. H'El shows up and attacks Superboy. Superboy realizes H'El is not nearly as strong as he was in the past. He figures out that if H'El is injured at one point in time, he will take damage in all points in time. As H'El dies in the past, H'El disappears in Argo city.
In Kryptonopolis, Superman meets his father, Jor-El. Only this is a Jor-El from both an alternative timeline and the future. This version of Jor-El tells Superman that he created H'El. Somehow, H'El survived the destruction of Krypton. With Krypton just minutes from destruction, Superman and Alterna-Future Jor-El travel deep into Krypton where they confront H'El. Superman realizes that H'El didn't just travel back in time; He'L gave himself the ability to appear in multiple points of time at once. Killing him, as Jor-El suggests, won't actually stop him. Superman freezes the suicide-weakened H'El in place using his super-breath. H'El is left at Krypton's core to have his molecules dispersed when the planet explodes. Superman returns to the present.
Superboy realizes Krypton is about to explode, and uses his powers to save Argo City by ripping it from Krypton's crust and hurling it into outer space.
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Kon-El was introduced during "Death of Superman" story arc in 1998. For 15 years, Kon-El had believed himself to be no more than a "living weapon", a freakish biological construct intended to destroy Superman. He worried about whether he actually had a soul, rights, or free will. He constantly second-guessed himself, even as he showed that he had a kind heart, strong moral code, and a powerful commitment to doing good even when everyone told him it was the wrong thing to do.
Realizing that Argo City won't just "come free" of Krypton of its own accord, Superboy/Kon-El realizes he is fated to die saving Supergirl and saving the future.
This is one of the most poignant scenes in comic book history.
* - Quite naturally, no one ever dies in comic books. Superboy/Kon-El is plucked from the moment of his death by a mysterious alien known as the Oracle, who has him patrolling time to ensure the damage H'El caused is rectified. He later returns to Earth. DC Comics just wiped him out again 2016 when Doctor Manhattan wipes out 10 years of DC Comics multiverse history. This allowed DC Comics to reboot its multiverse for the fourth time in 10 years. He never existed, which is sad -- because Kon-El was one of the most exciting things to happen to Superman in decades.