I think I remember learning that the people in the main round-up countries (as in, the countries where they rounded people up and put them on trains to the camps) knew that those people were taken and were not coming back, and that they kind of turned a blind eye to it. But did they know the extent of what was going on? Were they just afraid to notice it?

Bonus question: did any of the other powers have an inkling as to what was going on?