I'm feeling foul towards monotypes, but monoprints, my friends, those I adore.
A monotype is when you have no reproducible matrix. A monoprint is when only aspects of the print are unique to each impression, and a reproducible matrix is utilized in conjunction with it. For example, the David print below is a monoprint because the inking is unique to each impression, but the matrix is permanent and so reproducible. The prints of Cein below are monotypes, because they are paintings made directly onto smooth plexiglass in graphite etching ink and then printed.
But, they're still pretty good, at least for monotypes.
I also did two of Nate. I rather like his hat.