The European Central Bank yesterday, in the words of The Washington Post, "announced that it would buy the bonds of struggling governments without limit" (emphasis added). But that can really only mean "without an announced limit." There is an implicit limit so long as ECB sticks to its also-announced promise to neutralize the monetary-base-expanding effects of its struggling-government bond purchases by selling, euro for euro, other bonds from its portfolio, because its current portfolio is finite and only some of it is not already struggling-government debt. It is difficult to discover exactly what this implicit limit is in billions of euros.
The Eurosystem (the ECB plus the eurozone's national central banks) can purchase bonds of the struggling GIPSI (Greece, Ireland, Portugal, Spain, or Italy) governments in two ways: directly, or indirectly by making additional loans to commercial banks that purchase GIPSI bonds (and collateralize said loans with said bonds). To sterilize purchases of either kind, the ECB will have to sell its non-GIPSI bonds (or shrink its loans to banks collateralized by non-GIPSI bonds). The Eurosystem's reported balance sheet shows €3085 b in total assets. It does not reveal what percentage of its current assets are in GIPSI sovereign debts and GIPSI-collateralized loans. We can assume that the €279b of securities acquired under the ECB's two "covered bond purchase programmes" consists entirely of GIPSI bonds. For the sake of argument let's assume that gold assets (€434b) and foreign-currency assets (€312b) won't be touched. We can break the largest asset category, "Lending to euro area credit institutions related to monetary policy operations denominated in euro" into two parts: what was on the balance sheet two years ago (€592b) and what's been added in the last two years (€618b). Assume that half of the former and one-fourth of the latter is neither GIPSI debt nor the debt of borderline-struggling sovereigns like France and Belgium, but is debt that could be sold for sterilization purposes. That gives us a total of €450b as the upper limit of ECB purchases of the bonds of struggling governments under a policy of full sterilization.
This number is purely a guesstimate. But it probably isn't off by a factor of two. If the ECB finds itself wanting to make €1000b of GIPSI bond purchases, it is clear that the ECB will have to switch from sterilization to some other strategy for keeping M2 from ballooning, like the Fed's QE1 strategy of paying higher interest on reserves. Note that the ECB is already paying interest on reserves, and has been since its beginning, whereas the Fed started at zero.
For as long as it lasts, sterilization means that as the ECB buys more GIPSI sovereign debt, it will be shrinking Eurosystem credit to other borrowers, namely to private borrowers and to less-irresponsible sovereign borrowers. Starve the productive and the relatively prudent to lend to the unproductive and imprudent. That is not what anyone could consider a prudent mix of Eurosystem assets, nor a promising way to promote economic growth.