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 generalize 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 realized on minimal sets, and if the rotation interval has a 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.
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