How abolish the fractional reserves?

Abolish nothing apart from government monopoly privileges (legal tender, bank licences) and subsidies (central bank). In a free market, no one would have a special privilege to issue notes referring to non-existing commodities. Everyone (you, me, a firm, a "bank") would be free to issue whatever notes/claims they want. The market would price each note accordingly. If said notes are issued (exchanged) under false pretenses, that would amount to fraud. 

 

Savers of capital can easily meet with entrepreneurs and investors ready to employ it without issuing notes under false pretenses (fractional reserve banking). 

 

Both theoretically (logically) and empirically FRB can only end in two possible outcomes: (1) collapse of the Ponzi scheme as the amounts of property claimed overshoot the amounts in store, or (2) a central bank.

 

There is absolutely no need to "outlaw" FRB in a free market. If it's fully disclosed, then it will die off on its own. If it's performed under false pretenses, then it will die off as fraud.