The paper contributes to the investigation of epimorphisms in the category
of reduced partially ordered rings (porings), Two main questions are consid
ered: 1) Does the set of isomorphism classes of a given poring have a large
st element (an epimorphic hull)? 2) Given an epimorphic extension, or even
a Prufer extension. f: A --> B of porings: how closely are A and B related
to each other?.