When does X champion powerspike and what category do they belong in?

I'm a bit curious as to when a champion powerspikes or when they become their strongest in game be it from their items, level, or how their kit functions. I also want to know why they also powerspike at said moments too. I want to better understand what parts of the game does the champion shine in and what are they categorized as (lane bully, mid game champ, late game champs or hypercarries). For example: {{champion:58}} Renekton, {{champion:122}} Darius, and {{champion:80}} Pantheon are lane bullies. {{champion:103}} Ahri, and {{champion:4}} twisted fate are mid game champs. {{champion:268}} Azir, {{champion:10}} Kayle, {{champion:67}} Vayne, and {{champion:96}} Kog'maw are hypercarries. Of course not every champ can be categorized into certain parts of the game as some might have relatively stable power throughout the game or rely more on snowballing to get their powerspikes like most assassins. Some champs might also still be relevant even outside their powerspikes too depending on how their game goes and some champs Miss Fortune and Lucian are both lane bullies in bot lane but can still contribute a lot in the late game or Renekton having a mid game powerspike thanks to his Ultimate.
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