Let me just cough up some quotes from some champions' lores:
"Twitch came to the League of Legends to represent himself "as the only one of his kind" (...)"
"a being like no other emerged from the forgotten alleyways of Noxus."
"His search brought him across all the lands south of the Great Barrier, but everywhere he went, he was unique."
The are obviously some other "one-of-a-kind" champions: Shaco, Fiddlesticks, etc.
And now again:
"Fizz returned to find the city abandoned: his people had vanished, leaving Fizz without a clue to explain their disappearance".