  The main purpose is to characterise continuous maps that are $n$-branched
coverings in terms of induced maps on the rings of functions. The special
properties of Frobenius $n$-homomorphisms between two function spaces that
correspond to $n$-branched coverings are determined completely. Several
equivalent definitions of a Frobenius $n$-homomorphism are compared and some of
their properties are proved. An axiomatic treatment of $n$-transfers is given
in general and properties of $n$-branched coverings are studied and compared
with those of regular coverings.
