This is the second part of our study of epimorphisms with source a thick generalized
-gon and target a
thin generalized
-gon.
We classify the case
when the polygons are finite (in the first part (2022) we handled the cases
and ).
Then we show that the infinite case is very different, and construct examples
which strongly differ from the finite case. A number of general structure
theorems are obtained, and we also take a look at the infinite case for general
gonality.