We continue our study of the
c-K-structures introduced in Part I of this paper; these are triples (ϕ,Π,Π′) where
ϕ : Π → Π′ is a well-behaved incidence structure epimorphism. This paper is
concerned with uniformity and regularity of c-K-structures. We obtain connections
with PBIBD’s ARBD’s and transversal designs.