Darkseid was master of his domain on the planet of Apokolips, in a dimension adjacent to but not confined within the Earth-One universe. While his counterpart Surtur was manipulated by Earth-Two's Hitler into attempting to bring about the end of the dictator's world in a fit of vengence, Darkseid himself visited that world in order to restore himself while transporting his own world in place of Earth-Two. Thus, leaving himself unchallenged from his foes of New Genesis from his own dimension, Darkseid could reign supreme in a new universe. Remarkably, he once more recruited a Society of supervillains like he had on Earth-One, only unlike the Secret Society which had greater numbers and a more rebellious streak, the Injustice Society of Earth-Two yielded in submission to the power mad being. Regardless, in each instance his human servants failed fulfilling his schemes.
As for Surtur, after his minions were then vanquished by the Justice Society of Asgard version of the golden age super-stalwarts, he himself was defeated by their own combined might. This included migrants from another post-Crisis Earth who themselves offset the New Genesis heroes as well as Earth-Two transplants on Earth-One such as Doctor Fate (Doctor Chaos), Thunderbolt (Firestorm) and the Spectre (the original Spectre) However, due to the circular nature of time in that realm, this battle continued to play out for seeming eternity between the monolithic menace and the mighty meta-humans forevermore. In fact, at a certain point, an alien race bravely assumed the place of the Society in this never ending battle that left Earth-Two and... by extension all reality... protected, as the closet Surtur came to that planet was in the hazy clouds about a war-swept world in 1945.