  We study Hurwitz spaces with regard to homological stabilization. By a
Hurwitz space, we mean a moduli space of branched, not necessarily connected
coverings of a disk with fixed structure group and number of branch points. We
choose a sequence of subspaces of Hurwitz spaces which is suitable for our
investigations.
  In the first part, we introduce and study plant complexes, a large new class
of simplicial complexes, generalizing the arc complex on a surface with marked
points. In the second part, we generalize a result by
Ellenberg-Venkatesh-Westerland by showing that homological stabilization of our
sequence of Hurwitz spaces depends only on properties of their zeroth homology
groups.
