Conducting composite current collector for a battery or supercapacitor and production process

A composite thin film for a battery or supercapacitor, said composite thin film comprising graphene sheets dispersed in or bonded by an electron-conducting polymer network, wherein said composite thin film has a thickness from 2 nm to 500 μm and an electrical conductivity from 10−4 to 104 S/cm and wherein the graphene sheets occupy from 10% to 99% by weight and the polymer network from 1% to 90% by weight of the total composite weight, wherein said electron-conducting polymer network comprises chains of a conjugated polymer selected from poly(3-alkylthiophenes), poly(2,5-bis(cholestanoxy) phenylene vinylene), poly(2,5-dialkoxy) paraphenylene vinylene, poly[(1,4-phenylene-1,2-diphenylvinylene)], polyparaphenylene sulphide, polyheptadiyne, poly(3-octylthiophene), poly(3-cyclohexylthiophene), poly(3-methyl-4-cyclohexylthiophene), poly(2,5-dialkoxy-1,4-phenyleneethynylene), poly(2-decyloxy-1,4-phenylene), a derivative thereof, a copolymer thereof, or a combination thereof, or comprises polythiophene hydrogel polymer in a dehydrated state.