"the recent giant injection of ECB cash left banks awash with money but too scared to lend it."and
"With total ECB lending at 664 billion euros, banks are now storing over three-quarters of money lent by the ECB at the central bank, compared to around a third after the collapse of Lehman Brothers back in late 2008."Both statements give the impression that the size of the balance sheet of the central bank is driven by the actions of commercial banks. This is misleading. The size of the central bank balance sheet is determined by monetary policy. Monetary policy will react to economic developments, including actions of commercial banks, but at the end of the day the size of their balance sheet is mainly a decision of the central bank.
Towards the second week of December the ECB decided to increase lending to commercial banks (by making it attractive, of course). This led to an increase in the ECB balance sheet of about €250 billion between December 16 and December 23. This is associated with an increase in assets (lending to euro area credit institutions) as well as an increase in liabilities (accounting still works!). There are potentially two liabilities that could change: Banknotes in circulation (this is printing money) and deposits of commercial banks at the central bank. Currency in circulation barely changed that week, but deposits of commercial banks changed by about €200 Billion (the rest comes from other liabilities). As banks get loans from the central bank, their accounts at the central bank get credited.
Since then, not much has changed. Loans to banks remain high as well as deposits from banks. What if commercial banks start lending to the private sector, will the level of deposits at the central bank go down? Not necessarily. The only way for the level of deposits to go down is if commercial banks start paying back the loans they took from the central bank. And the central bank could always resist this move by making these loans even more attractive (this is standard monetary policy).
So it should be no surprise that deposits of commercial banks at the ECB are at a record high when the balance sheet of the ECB is at a record high (we observe the same phenomenon in the US or England). When monetary policy decides to increase its balance sheet, both the liabilities and assets have to increase. Given that central banks are not massively increasing notes in circulations, it must be the case that it is the deposits of commercial banks at the central bank the ones that are increasing.