A Greek exit from the eurozone would be a social, political and economic cataclysm. It would also make a mess of the Eurosystem, the carefully constructed central-banking arrangement that underpins the 19-nation currency union
How are central banks set up in the eurozone? 
What we think of as the European Central Bank is really the “Eurosystem”: the 19 central banks of eurozone countries plus the ECB itself. The vast bulk of ECB’s balance sheet—its assets and its liabilities—is held by the national central banks. They function as sort of branches of the broader ECB. This is a consequence of Europe’s imperfect union: All the eurozone countries retain their own central banks and their own banking systems, even though the system’s policies and rules are set centrally.
In normal times, this is a distinction without a difference. But when one country is on the cusp of leaving, it starts to matter.
How do commercial banks operate in the eurozone?
They interact and transact with the central bank of their home country.
Commercial banks have their own deposit accounts with the local central bank. When they need central-bank loans, they turn to the local central bank. That means that, say, Piraeus Bank (a Greek bank) gets funding from the Bank of Greece.
A customer’s deposit in a commercial bank is simply an amount the bank owes the customer. When a customer of Piraeus Bank transfers €1,000 ($1,117) to another Piraeus Bank customer, Piraeus notes in its ledger that it now owes €1,000 less to Customer A and €1,000 more to Customer B.
When the Piraeus customer transfers €1,000 to a customer of Alpha Bank (another Greek bank), the Bank of Greece gets involved.
Just as a customer deposit with Piraeus is an amount Piraeus owes the customer, Piraeus itself has a deposit account with the Bank of Greece that shows how much the Bank of Greece owes it.
In the transfer from a Piraeus customer to an Alpha customer, the Bank of Greece notes in its ledgers that it now owes Piraeus €1,000 less and Alpha €1,000 more. Piraeus notes that it owes its customer €1,000 less and Alpha that it owes its customer €1,000 more.
(This, incidentially, is why electronic transfers within Greece are permitted by the capital controls.)
OK, so what happens if a Piraeus customer transfers €1,000 to, say, an account in Germany with Deustche Bank?
Well, the customer can’t anymore because of capital controls, but let’s go back to a time when he or she could.
Piraeus deals with the Bank of Greece and Deutsche Bank with the Bundesbank, Germany’s central bank. That makes the transfer more complicated ...
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