I remember some attempts to achieve that, do not have source anymore. The whole idea was to take two electrodes and grow thick forest of graphene tubes on them

I remember some attempts to achieve that, do not have source anymore. The whole idea was to take two electrodes and grow thick forest of graphene tubes on them massively increasing surface of electrodes. But to get even close to batteries, electrolyte was necessary, however pouring electrolyte onto electrodes modified in such way caused graphene tubes to break off and create shorts. So ultimately went nowhere. Maybe if it would be possible to grow graphene in the electrolyte directly.