On his blog, JP Koning discusses the case of Somalia which has managed without central bank issued money for decades.
Old, legitimate notes and newer, counterfeit notes trade at the same price which equals the cost of producing counterfeits.
See also this previous post.
In the FT, David Pilling reports about Somalia which has managed without central bank issued money for decades.
… up to 98 per cent of local banknotes are fake … With the help of the International Monetary Fund, Mogadishu plans to print official banknotes for the first time in more than a quarter of a century … No official Somali currency has left the presses since the Horn of Africa nation descended into clan warfare after the collapse of the government in 1991.
… warlords, businessmen and breakaway regions printed counterfeit notes or shipped them in from abroad. … several important issues, including what the government would use to back its new currency, were still being discussed. So was the question of what the conversion rate would be of fake Somali shillings for the new official ones. Use of Somali shillings, largely limited to the less well-off rural population, comes a poor third to US dollars and electronic money in what is a mostly dollarised economy. … Some dollars in circulation are also fake …