Base money is currency plus bank reserves. These show up on the liability side of the central bank’s balance sheet. Assets, including loans taken out by banks at the central bank, show up as assets on the central bank’s balance sheet. If banks borrow from the central bank and then take their reserves and use them to buy other assets, the liability side of the central bank’s balance sheet will fall while the asset side will stay the same. In other words, the central bank will build equity.
American banks have been holding the excess reserves created during the crisis, so the Fed’s balance sheet hasn’t changed. If European banks have been selling their reserves to buy other assets, then the monetary base and the liability side of the ECB’s balance sheet would shrink while the asset side would stay the same..
The same thing would happen in America, if American banks took their excess reserves and bought other assets, made commercial loans, bought real estate, etc. then the monetary base and the liability side of the Fed’s balance sheet would shrink but the Asset side of the Fed’s balance sheet would not change.