Team Bot Lane Pen!
So basically a friend and I wanted to just play a bs bot lane (and because I wanted to try Karthus out more) this is what we did:
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So while it's not too meta breaking, it's not a bot lane anyone has probably seen in awhile. The reasoning behind this:
Penetration
Karthus's W reduces magic resist by 15% which pairs well with Corki's magic damage (especially early) and the slow allows for constant stream of damage from Corki as well. Karthus can provide poke and if he dies, the enemy can't really continue with any fights due to his pressure from his passive. So it'll usually end in a 1 for 1.
Moving on beyond the early levels: With the recent changes to Corki as well as our penetration-inspired lane he decided to go from Trinity Force -> Youmuus -> Black Cleaver (easily proc'd from E)
It's also important to note that Corki is granted a buttload of cdr from these first 3 items
At this point, no amount of resists could stop our damage (which is pretty reliable, especially once Karthus completes Rylais). There is a decent amount of peel with Karthus's two slows and Corki's self peel in his kit.
Corki also built
which paired nicely with my 
Final Builds
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(regularly buying pinks)
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Let me know how viable this bot-lane synergy actually is, what other comps have players devised with friends?
Take this with a grain of salt: I only have 1 game of experience with this and the enemy team played pretty bad tbh. All of this is pretty much still theoretical but it certainly is interesting.