Mid is the most conventional place for Karthus. His potential for damage can make him a hypercarry if you're smart about when to use E, and if you're accurate with Qs.
if u play him on ADC just act like a ADC kinda like Samira. hard to understand but Karthus deals so much DMG sometimes u just die for nothing and sometimes u get a few kills.
But if u asking how to script with him, its not worth, and not funny. general u need movement for every champ. go in Normals and test it out, dont ruin games in rankend when u dont know how to play