Disclaimer: I do not own Dragon Ball, or any of its associated characters and lore. That right belongs to Akira Toriyama.
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The Second Coming of Bardock
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East District, Mount Paozu, Planet Earth, Age 749, September 1
Driving her car at a fast rate, Bulma was so eager to find her third Dragon Ball that her car unexpectedly stopping threw her in for a loop. Checking around, she saw that her car didn't ran out of gas, but was caught in some kind of energy field generated by a handsome young man around her age with spiky black-hair.
"You might want to be careful there, beautiful." The youth said with a charming smile that captured Bulma's heart as much as his words and other looks. "You could've gotten in a huge accident of some sort at that speed."
Bulma blushed out of both embarrassment and a lovestruck feeling as she replied. "Sorry, I guess I got too excited there." Quickly turning off her car and exiting the vehicle as the charmer released his psychic hold on it, Bulma stepped forward to her new crush and introduced herself. "My name is Bulma from West City. Who are you?"
The local man's charming smile grew wider as he took his left hand to cup Bulma's blushing face while his other hand brought her closer to him. "My name is Kakarot, but you can call me Sweet Lips." He then brought his lips in for a kiss as Bulma energetically reciprocated the move and they engaged in intense lip-lock that lasted for half a minute until an older voice called out.
"Kakarot!" Exclaimed a suddenly appearing elderly man that spurred Kakarot to break the kiss and then change from someone around Bulma's age and height into a shorter and younger, yet flying off the ground, version of the person that took Bulma's first kiss much to her shock and eventual horror.
"Ah!" She screamed as she threw the faker away from her. She then proceeded to spit out any and all saliva she got from him before she then pointed angrily at him and yelled. "What the Hell was that?! If we were in the city, I'd probably be arrested for something as stupid as frenching a minor!"
"I'm not a minor, I'm twelve years old!" Kakarot retorted in annoyance before he showed a fiendish smile. "I just figured when I divined a girl with your good looks coming along, that this would be a good way to lose my first kiss. Don't pretend you weren't enjoying it."
"Shut up!" Bulma stammered in embarrassment and anger before she then turned to the old man. "If this brat's yours, I expect you to make amends, now!"
"Good grief." A new voice commented as Bulma soon saw a new person that looked almost exactly like an adult counterpart of Kakarot in armor appear out of nowhere. "My son sure knows how to pick them, and he hasn't actually mated yet."
"Bardock, don't encourage him, you hardened ghost." The old man admonished as he glared at Kakarot's newly appearing father.
"Uh, ghost?" Bulma asked in confusion as she stared at Bardock.
Seeing her complex expression, Kakarot shrugged as he explained. "Yeah, when Dad was in his last moments as a living Saiyan, he psychically transferred his own psychic abilities to me and has literally never left since."
As Bulma took her time processing Kakarot's words, the old man made a humph as he turned away from Bardock in exasperation. "While I am still grateful that you being here kept me from going flat, if Gine were here, she and I would have lots of words about your conduct as a parent as well as a person."
"Don't start with me, Gohan." Bardock seethed in restrained anger.
"Oh, what have I gotten myself into?" Bulma couldn't help but whine at the whole situation.
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Thought of this from looking back on some similar stories that have Gohan and Raditz inheriting Bardock's Kanassan-derived Divination ability while listening to Kung Fu Panda music. Don't know if anyone aside from myself wrote Psychic Goku before, but I hoped this looked interesting in its own way.