  We study quasiperiodically forced circle endomorphisms, homotopic to the
identity, and show that under suitable conditions these exhibit uncountably
many minimal sets with a complicated structure, to which we refer to as
`strangely dispersed'. Along the way, we generalise some well-known results
about circle endomorphisms to the uniquely ergodically forced case. Namely, all
rotation numbers in the rotation interval of a uniquely ergodically forced
circle endomorphism are realised on minimal sets, and if the rotation interval
has non-empty interior then the topological entropy is strictly positive. The
results apply in particular to the quasiperiodically forced Arnold circle map,
which serves as a paradigm example.
