Scenario 1: Vegeta kills Gohan as soon as he sees his potential.
Scenario 2: Vegeta sees the brat's potential as a chance to fulfill the Super Saiyan prophecy and overthrow Freeza.
Over the years, he teaches him everything about Saiyans history, ways and pride. Considering his age, Gohan is
eventually brainwashed and forgets about Earth.
Back on Earth, Chichi holds Goku responsible for Gohan having been abducted and asks for a divorce. Goku starts
blaming himself, loses interest in life and becomes careless, so, at some point, Piccolo kills him with a special
beam cannon attack.
Piccolo takes over Earth. Even though he hasn't totally abandoned evil, because of his experiences so far, he's less
simple minded and one sided than his father, so, instead of just brainlessly causing havoc, he rules the planet as a
king with an iron fist. In the meantime, fearing that the Saiyans might return someday, he keeps training himself
and spawns warriors in order to have an army of defenders for the planet when that day comes.
The news about a possible future Saiyan attack are spread across the planet. Humans acknowledge the peril is more
urgent than their grudge against Piccolo, so they join the demons' army. So does Dr Gero; with Goku dead, he does
not want revenge and he acknowledges that, if Saiyans destroy Earth, there will be no world for him to conquer.
5 years pass. For plot sake, Gohan's power is at the hundreds of thousands.
One day, Freeza humiliates Vegeta by beating him up, in order to punish him for something he did wrong. Gohan
sees that scene and goes mad, his power briefly soaring to one million or so. He kills Freeza before the latter can
transform.
Icers' empire is replaced by Saiyans' empire and Vegeta becomes the emperor. Gohan doesn't kill him. Even though
he's brainwashed into evil, Vegeta is the only family he can remember of, the only person who showed him some
affection in the loveless world he has lived, so he remains loyal to his mentor.
Vegeta decides to attack Earth and collect Kakarrot so that one more Saiyan will be added to the empire and help
them remultiply their race. The empire is crushed by Earth forces: humans, the demons' army and Piccolo, who reveals
that he allowed Dr Gero to turn him into a cyborg.
Piccolo recognizes Goku's son. Gohan is crying, begging for his life. Humans realize this child is just a misguided soul,
that it's not his fault that he became evil. They plead Piccolo to spare his life. Piccolo decides to integrate him to his
army.
Peace is restored on Earth. Gohan becomes Piccolo's student and, eventually, unlocks Super Saiyan transformation.
7 years later, when Babidi appears, Kami senses the danger and guesses it's time he and Piccolo become one again.
With his new power, on top of him being a cyborg, Piccolo is a match for Dabura, but Babidi majinizes him.
Piccolo is not totally controlled by Babidi; he damages Gohan enough to give him energy to awaken Buu but, in the
end, refuses to kill his student. Buu awakens. Babidi's like 'if Piccolo doesn't take orders, I don't need him' and orders
Buu to kill him. Piccolo tries to defend Earth and dies in a way similar to Majin Vegeta.
Over the following 2 days, Gohan trains in ROSAT while Buu is having fun on Earth (he kills Babidi at some point during
those 2 days). When he gets out, he's unlocked SSJ2 and is as strong as his post Z sword self in canon. He starts fighting
Buu and holds his own. During the fight, he sees himself in the djinn; Buu is a lost soul as he used to be. Even though
he's angry at Buu for having killed Piccolo, he remembers that, himself, he had his second chance, so Buu deserves one
too.
Buu is convinced to change his ways and makes friends with Gohan, who becomes the new king of the planet. The series
ends with a scene of Goku and Piccolo sparring in Heaven and being happy that Gohan, whom both of them have been
fathers to, has found his inner peace.