Disclaimer: I don't own the Dragon Ball franchise or it's related concepts and characters, but Akira Toriyama and his affiliates do.
The Earthrealm Empire's Victories
Imperial Directory Building of Planet Machina, formerly Doctor Myuu's Lair on Planet M-2, Age 789
In the forty years since Kakarot's first Dragon Ball wish, the Earthrealm Empire under his rule had emerged as a rising intergalactic power built on force and knowledge as much as political cunning. With Kakarot at the throne of Earth and it's increasing number of subordinate worlds, conquered, colonized, and willingly joined alike, the Frieza Force surrendered with their Emperor's death at Kakarot's hands, and the Galactic Patrol had become begrudging allies of his Empire. Upon learning of the Machine Mutants and the potential threat they posed, Kakarot ordered for their puppet cult on Planet Luud to be purged and for a surprise attack on Planet M-2 to be launched. Although the Machine Mutants' resistance to Earthrealm's offense was strong, in the end, Kakarot had called forth the Dead Zone to suck up the more rebellious of their forces, including their creator and de facto manipulator, and then laid claim to the planet which he had rechristened Machina.
"So how goes Capsule Corporation's efforts, Chi-Chi?" The Earthrealm Emperor asked his Empress in a newly refurbished suite accustomed to dignitaries such as them, their two sons, and their daughters-in-law.
Although slightly annoyed that her husband was concerned about their duties and subjects at the moment when it was just the two of them, Chi-Chi replied nonetheless. "Bulma told me that she and her people are already taking charge over the remaining Machine Mutants and studying their technology as we speak. So far it's going smoothly."
Nodding with a satisfied grin, Kakarot said. "Excellent. Since this year will be their company's seventy-seventh anniversary, I'm thinking of giving control over this planet to Trunks. I'm sure he'll do a fine job."
Chi-Chi showed a coy smirk at that. "Free of charge, huh?" Seeing Kakarot nod, she then said. "And what do I get?"
Smiling knowingly, Kakarot brought his lips to his wife's. Once the kiss passed, he replied. "That among a lot of great things, darling."
Elsewhere in the Directory Building, Kakarot and Chi-Chi's first-born heir, Gohan, was enjoying drinks with his Imeckian wife, Sheela. While Gohan probably would've married someone of his own choosing, regardless of class, Kakarot encouraged for both of his sons to interact with highly prominent personages from Earthrealm's other member worlds than just Earth alone to insure trust among the numerous species that called the Empire their home. Thankfully, Kakarot was understanding as he was focused on political tactics, and therefore allowed such bonds to happen gradually which they did. Sheela herself wasn't a princess of her own people compared to Goten's Gelboian wife Leena, but upon the restructuring of Imecka's government with the downfall of Don Kee, she had acquired great renown with her populace and Earthrealm's leading classes that she was more than welcomed by Kakarot as a candidate for Gohan's wife.
"Looks like things are on a good roll for us, Sheela." Gohan commented to his wife as they observed a small party to the recent battle's victors.
Sheela chuckled before turning to Gohan with a flirtatious smirk. "And what about you and me, Gohan?"
Taking another sip of his drink, Gohan then brought his head to his wife's before they kissed for a brief, yet good, moment. "I'm thinking of being a father, Sheela." He admitted with a shy, yet genuine, smile.
"We can arrange that." Sheela assured with an expecting grin.
Outside the Directory Building, Goten and Leena used their energy to fly over the city in interest.
"Well, I got to give that Myuu guy credit, Leena." He admitted to his wife in midflight. "He knew how to build an advanced city."
"Apparently so." Leena replied. "Hopefully, your father will find good people who will manage it well."
"I'm sure he will." Goten than brought Leena in his embrace with a smile. "But for now, let's not talk about politics."
Smiling back, Leena kissed Goten before then saying. "Want to spend the night doing something even more productive than usual."
Blushing widely, Goten eventually replied. "Yeah, let's do that."
Hope nobody minds the Mortal Kombat reference. It was the closest I could get to a name for any regime Goku/Kakarot would make on his own without overthrowing any of the "tyrants" in the franchise. Anyway, I figured that Sheela and Leena would be fitting for Gohan and Goten because, as far as I could tell, they'd be around the same age compared to Goku who'd be in his fifties by the time GT occurs. Anyway, I've got six more Dragon Ball one-shots to do, and then I'll see what I can do after that.
For FFN readers, I'm placing this in a separate category than usual because the website is kind of stingy on who goes where, if you know what I mean. I'm thinking of doing the same thing with my other one-shots and potential full-length stories as well.