Who limits the euro issued in each eurozone country?

Question

In my understanding each member of eurozone prints their own euro. How was it decided how much euro will be printed by each country per year?

Also, for weak eurozone countries, what is preventing them from printing more euro and diluting its value without the permission of eurozone money policy maker? Of course there is someone who will check but it can be introduced incognito to the market. Does eurozone have some kind of secret service agency that checks it?

Sub question: How does it work, especially for the initial introduction of euro, which country have which amount of euro. How about for each new member, how many euro will they allow to be exchange per their original currency?

Answer 1

Only the ECB has the right to issue Euro banknotes (p. 103). States can issue coins up to a total value set by the ECB.

At some point during the initial creation of the Euro, and during the accession of new members, the exchange rate is set. From that point, swapping the paper is merely an administrative task.