  We generalize the results of arXiv:1212.1875 and arXiv:1212.6919 on
attraction basins and their boundaries to the case of a specific class of
rotating black holes, namely the ergo-free branch of extremal black holes in
Kaluza-Klein theory. We find that exact solutions that span the attraction
basin can be found even in the rotating case by appealing to certain symmetries
of the equations of motion. They are characterized by two asymptotic parameters
that generalize those of the non-rotating case, and the boundaries of the basin
are spinning versions of the (generalized) subttractor geometry. We also give
examples to illustrate that the shape of the attraction basin can drastically
change depending on the theory.
