The way I have learned it works is that if a bank running a fractional reserve is having a bank run, they will turn to the governmental controlled banks to have more money transferred, so they can cope with all the withdrawals, but could not a state bank just print digital money out of thin air to cope with the demand for withdrawals ?
Let me put it this way. Banks create money not out of the thin air. They create money out of yours and mine signatures on the mortgage applications and on credit card applications and on loan applications etc... Now, when you an I tell the bank to go and take a hike because we gonna default, the money created out of those signatures are magically disappearing.
What do you think central banks were so busy with lately? Yep they were busy resigning all those debt applications which went bad into their own name. This process has been called many names TARP, QE1, QE2, QE3 etc.... The moment they stop doing it we will have humongous deflationary collapse i.e. lots of the money created out of debt will simply disappear, causing more defaults and more disappearing money. This is kind of a bit too scary for the central banks and their puppet masters, so they hope to be able to take over all those defaulted debts in order to preserve money.
Amount of money they create this way is only limited by amount of new debt the system able to consume. This is exactly why the only way to fix the debt problem is by creating more debt. And this pyramid is mathematically certain to come crushing down eventually even if the eye on the top wants to do it's damnest to postpone it for another day.
Of course, there is also zimbabwe route. Just start printing paper notes with a few extra zeroes on them. 6 or 10 will do the trick perhaps. Also need a few helicopters to deliver it all to the population. Problem solved.