Forgive me if this should have been a dm, but may I request that essay about Gohan and Vegeta’s relationship?

Ohohoho well SINCE YOU'RE ASKING.

Consider Vegeta. He has always prided himself on being, even as a child, stronger than all adult Saiyans, and that without training under anyone. He was a prodigy! He was unrivalled! And then he meets Gohan who 1) is probably even younger than Vegeta was when he was declared the best 2) never had any training whatsoever either AND wasn't even born and raised in a warrior culture. When do they first meet? Oh, that would be when Gohan absolutely trounces Vegeta's ass at the tender age of four years old (or five years old according to some Western translations, or three years old according to Toriyama's original concept), eliciting in Vegeta the same response Gohan gets from just about anyone: disbelief. For all that Vegeta has become the archetype of the shonen rival who always comes second, we tend to forget that he did beat Goku the first time they met -- and he beat him by a lot. He was torturing him to death when Gohan and Krillin and Yajirobé intervened, and without them Goku would be fucking dead (again).

Vegeta has thus been rattled not just by Goku but also by Gohan, who displayed enormous amounts of raw power at a ridiculously young age. And for all of Vegeta's posturing and pride, he noticed. After he allies himself with Krillin and Gohan on Namek, he shouts at Frieza that they're worthy allies because they're constantly becoming stronger, "especially the young one [who has] powers he can't even dream of". Gohan looks noticeably struck by this comment -- in the middle of the chaos of Namek where everyone is five times his height and a million times his power, Vegeta's acknowledgment would in a weird way probably mean a lot to him, especially since The Prince Of All Saiyans wouldn't say that kind of thing lightly. Gohan remains terrified of Vegeta's immense power and ruthless violence; but he takes Vegeta's profession of alliance seriously and doesn't hesitate to dive into danger to drag Vegeta out of the way, a move which completely baffles and infuriates Vegeta -- it was probably the first time anyone ever saved his life in combat. Of course he shouts at Gohan for what he can only perceive as a humiliation. And yet later, against Frieza, Vegeta does exactly the same thing for him, for no clear reason other that he considers Gohan an ally worth preserving.

So from the beginning, despite Vegeta's pride on one hand and Gohan's fear on the other, there's a warriorlike respect between them, and they're changing each other. Vegeta loathes Goku and dreads Frieza, and despises just about anyone else he fights... but not Gohan. That doesn't mean he's nice to him; when Gohan adorably tries to thank him for his help post-Namek arc, Vegeta batting his hand away is basically the continuation of his confused anger at Gohan trying to save his life. He cannot see that extended hand as anything other than an insult to his strength. But with that move, Gohan is literally the only fighter who tries to... befriend Vegeta. All the other Z-fighters keep well away and Goku sort of lost interest the moment he heard of someone stronger. But Gohan takes the time to thank him and acknowledge that Vegeta went out of his (admittedly very narrow) way to help them. I like to think that his wounded surprise when Vegeta rejects him would quietly shock Vegeta in turn -- shit, that kid really was trying to make friends. So his mental Gohan file would boil down to 1) Incredibly strong and worthy ally 2) Too sweet for his own good.

During the Cell arc, Vegeta's posturing endangers everyone. Once again, Gohan's amazing untapped strength comes out in full force, and once again he risks his life to save Vegeta's. But instead of blowing up at him this time, Vegeta apologizes (which shocks everyone who hears it). Is it the only time we see Vegeta apologize onscreen? I think it is. And he calls himself dead weight! Calls himself a burden on Gohan! Even in the deepest depths of his self-hatred, he would have never said something like that to Goku. No one but Gohan could have ever elicited that from him; no one but Gohan was both strong enough to actually protect Vegeta, and sweet enough that not even Vegeta could resent him for it.

So the little seed of respect planted during the Namek arc has been quietly growing during the Cell arc, and we see hints of it during the Buu arc too -- when Gohan is presumed dead, Vegeta is straight-up distressed, basically saying that Gohan didn't deserve it, getting hit by the guilt of what he's done. Gohan was the only Z-fighter to acknowledge Vegeta's humanity, and in return Gohan is the only Z-fighter whose humanity Vegeta acknowledges.

And then Buu is defeated, Vegeta concludes his character arc, and has his last interaction with Gohan in DBZ: they meet before the final tournament and Vegeta coldly tells Gohan he clearly hasn't been training. And Gohan seems intimidated and embarrassed. It's clear that for all of Vegeta's repeated fuck-ups, Gohan has never stopped respecting him: in his mind, Vegeta is still that pillar of strength that almost annihilated them all that first time on Earth, and saved their asses multiple times on Namek when Goku was nowhere to be found. The fact that Gohan is so vulnerable to Vegeta's judgment harks back to that moment on Namek when Vegeta casually acknowledged how awesome Gohan's power could become. Gohan remembers that -- and now, having abandoned his training, he clearly feels that he's disappointed Vegeta.That he didn't live up to his hopes. And Vegeta, in turn, clearly tells him he expected better -- that he did have hopes of Gohan, and that Gohan is fully capable of (and therefore responsible for) upholding Saiyan pride.

This is when we leave canon and depart for the mad fevered realms of my brain. The Namek Chief and Old Kai both saw deep untapped potential in Gohan but could only attempt to bring it up to the surface through magic. Gohan is basically, repeatedly confirmed as the strongest DBZ character ever... if he could only manage to actually unlock that strength. But it's locked up tight.

I wonder if anyone could HELP WITH THAT.

Being drafted in a terrible war at an absurdly young age? Vegeta knows how that feels. Being hindered in your ability to get stronger because of psychological issues stemming from trauma and self-doubt? Vegeta also knows how that feels. Feeling like you can never unlock your abilities when you need them? Vegeta also knows how that feels! He can even relate to being disgusted with fighting -- he swore to renounce fighting after Goku's second death and essentially kept his word right up until Goku came back. Most importantly, Vegeta would be uniquely suited to recognize how both Piccolo and Goku's training approaches fucked up Gohan. Piccolo didn't reassure him enough, turning the fight into this terrifying non-negotiable obligation. Goku reassured him too much, basically taking the fight aspect entirely out of Gohan's training -- to the point that Gohan experienced the actual fighting as a betrayal when the time came to face Cell, and terrified himself when his Saiyan ferocity came out unbidden and uncontrollable.

As the only person alive to remember Saiyan culture, Vegeta could see that what Gohan's been missing is the sheer joy Saiyans are supposed to experience when fighting. And post-Buu arc, Vegeta has grown enough to acknowledge he can care for other people. He would allow himself to actually use everything he knows to further someone else's development. His skills as a prodigy, his understanding of Saiyan nature, his own exploration of trauma, his respect for Gohan and his faith in that famed potential -- all that could come out to play big time. He could help Gohan; he would help Gohan. And thus finally return the friendship Gohan dared to extend to him all those years ago. And when I think of how Gohan would react to that, I CRY.