I wanted to set some things straight. There has been a lot of debate regarding this, and I have decided to put forth my argument for why AP Gragas is the highest skill cap champ in the game.
Let's talk skillshots. But not in the conventional way. Indeed Gragas has 3 skillshots, including his ultimate with the ability to push enemies towards or away. With deeper consideration, the only skillshot a good Gragas player can use without thinking about it is his Q (the barrel), because there are no consequences other than losing mana for a missed barrel.
But for his other two skillshots, they have severe consequences. Whenever Gragas uses his e, or his bodyslam, there can be extremely bad consequences. An aggressive body slam into the other mid can put you completely out of position, and in team fights, the same occurs. Body slam is a huge vulnerability, and is extremely dangerous to use because it puts Gragas into the enemy's range. Only when escaping or dodging does E not have any real consequences, and is a great skill. Now, his ultimate is the extremely high skill cap ability. It has the ability to make or break a team fight. A key target can be either blasted away from the team, or knocked into Gragas' own team. Also considering the fact that it can miss, this is a huge deal. I'd argue that no Gragas hits all of his ults perfectly in a game, because this is the hardest skill to aim, CONSIDERING so many champs in this game have a quick movement ability that can completely offset the ultimate. Also a golden opportunity can become deadly, as an ultimate that pushes their tanks into your team.. I've seen it happen. It is like a blitzcrank pull of amumu. The team fight is lost.
Because he has such consequences for his abilities, he is the highest skill cap champ.
For those of you who say Anivia is the hardest.. With blue buff she has to make very little decisions, its just spam ultimate, q as needed, w and e as needed. Yes, the wall is really cool and it takes skill to aim that, but there is not as devastating a consequence for screwing it up, compared to body slam. Anivia as well as other ap mids do not need to make decisions, they simply need to spam abilities to win the game. This is why Gragas takes the throne for the highest skill champ in the game.