I have been wondering this for a while, but it seems that you and the other printers place one print directly on top of another, immediately after you have finished making an impression. Sometimes you would also flip over the prints and lay them down on top of the blocks to inspect.

Do the pigments not transfer from one sheet to another, or from the block to the back of a sheet? I guess I am thinking from the standpoint of screen printing, where you often have to be careful while the paints are still wet to keep them from all sticking together and ruining the prints.

There is no pigment transfer at all from sheet to sheet. The action of the baren on the back of the paper drives all the pigment/paste down into the depths of the paper - we are using a fluffy washi, not a flat calendared paper - and there is nothing left to smear. We can even rub the surface with our hands ... nothing will smear.

As for transferring from the block, again, there is nothing left behind after the impression has been taken. Down in the 'valleys' is still wet of course, but the wood surface itself is now clean and dry.