Are World Champion Winners Allowed to Pick Skins That Already Have a Worlds Skin?
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Not sure. It's been enough seasons that overlap is happening in key champs from some seasons. I don't know if players would want to choose a champ with a champion skin already though. Would feel like you copied perhaps.
Up until last year... No. But then Riot started to get a lot of community backlash from it. So they started to make it a much larger collaborative process in which the players are hands on helping them design everything. So you can expect that the players will have a lot of input on what skins they want.
Here's the VidDoc about the last skinline that they did. They go a little more in depth with how they're going to do things for the world champs from now on.