It would run off our mobile devices and PC sort of like bitorrent.
I am aware of webtorrent (web based torrenting p2p) for videos and such but still nothing in production.
IMHO, the next person that comes up with a highly scalable, decentralized, widely distributed mesh network of devices to securely transfer files between peers will not be a rich man but he would be a hero, I personally would donate a large chunk of money just to keep it afloat for others.
Sort of like a "public funded public utility" software.