From the WSJ:
Most euro-zone central banks maintain at least limited capacities to print bank notes. While the European Central Bank is responsible for determining the euro zone's supply of bank notes, it doesn't actually print them. The ECB outsources the work to central banks of euro-zone countries. Each year, groups of countries are assigned the task of printing millions of bank notes in specific denominations.
The countries have different arrangements for printing their shares of the notes. Some, like Greece and Ireland, own their printing presses. Others outsource to private companies.
The assignments vary from year to year. Last year, Ireland printed 127.5 million €10 notes, and nothing else, according to its annual report. This year, it was among 11 countries assigned to print a total of 1.71 billion €5 notes.
Full story here.