This info can be found, probably in places all over the forum, but here it is:
For the introduction of the Euro, every country that joined printed all denominations, except Ireland (no

) and Portugal (no

and

).
In the years since (2002 - now) every country has been given just a part of the production, generally 1 to 3/4 denominations per year ("small" countries to "large" countries/Germany). Some countries really stick to the same denominations every year (Belgium and Greece the best examples), Germany has now printed every 7 over the years.
Then Duisenberg stepped down as president and Trichet replaced him. This was in end October/begin November 2003. Some of the 2003-printed notes may have the Trichet signature already. I know that for the German

and the Austrian

have a plate number (the first three numbers of the short code) with both signatures, but the same number can be used in more than one year. I'm not sure on this, though. All 2004 notes should be with Trichet signature.
On the other hand, when I was in Ireland (2008) the vast majority of

(49/76) were Irish, some of them in uncirculated condition, all of them with Trichet signature. These were from the 2006 production.
I've only found 1 K/T

with Duisenberg signature, sometime ago here in the Netherlands.