We continue our discussion of perfect and scattered subsets in the generalized Cantor space. We give some properties of the \kappa-topologies over 2^{\lambda} introduced earlier (for \kappa \leq \lamba), define a Cantor-Bendixon process for forests, and begin work on showing the consistency of Cantor-Bendixon theorem analogues for closed subsets of 2^{\kappa} and P_{\kappa^+}\lambda, for \kappa regular.