Banking history: how did central banks and commercial banks become separate?

What happens if one day all depositors come to the bank at the same time and ask for their money? The bank has lent out most of the money, and only a little is left in the till. This question determined the structure of the 20th-century banking system.

1. The two-tier system. Today in most countries the central bank stands at the top, and below it are the commercial banks that serve the public and businesses. A commercial bank takes deposits and makes loans, while the central bank watches over the stability of the whole system.
2. A crisis was the trigger. As the US Federal Reserve history website writes, the Federal Reserve System was created in 1913 in response to a history of financial instability. Before that, because of the Panic of 1907, the temporary Aldrich–Vreeland Act was passed in 1908.
3. The Federal Reserve Act. President Woodrow Wilson signed the act on 23 December 1913. The act created 12 federal reserve districts, each with its own Federal Reserve Bank.
4. An old bank, a new role. The Bank of England, founded as a private bank in 1694, was taken into state ownership in 1946. The bank's museum calls it the bank that served as a model for many of today's central banks.
5. The "last resort" idea. One of the central bank's main tasks is to keep the system from collapsing when commercial banks temporarily run out of money. That is why the central bank is also called "the banks' bank".
6. The business of commercial banks. They attract depositors' money, lend it out and earn income from the interest margin. The main risk in this business is liquidity: being able to meet obligations with cash at the required moment.

Example (prepared by the author, hypothetical figures). "Navro'z Bank" has deposits of 1 000 units, of which 850 units have been lent out and 150 units are in the till. A rumour spreads, and in one day depositors ask for 300 units. The money in the till is not enough, and loans cannot be called back in a day. In a two-tier system, in such a situation the bank can ask the central bank for short-term funds. In periods without a central bank, such a situation often ended with the bank closing.