Decomposability problem on branched coverings

Given a branched covering of degree $d$ between closed surfaces, it determines a collection of partitions of $d$, the branch data. In this work we show that any branch data are realized by an indecomposable primitive branched covering on a connected closed surface $N$ with $\chi(N) \leq 0$. This shows that decomposable and indecomposable realizations may coexist. Moreover, we characterize the branch data of a decomposable primitive branched covering.
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