We assume a data set that is vertically decomposed among several servers, and a client that wishes to compute the skyline by obtaining the minimum number of points. Existing solutions for this problem are restricted to the case where each server maintains exactly one dimension. This paper proposes a general solution for vertical decompositions of arbitrary dimensionality. We first investigate some interesting problem characteristics regarding the pruning power of points. Then, we introduce vertical partition skyline (VPS), an algorithmic framework that includes two steps. Phase 1 searches for an anchor point Panc that dominates, and hence eliminates, a large number of records. Starting with Panc, Phase 2 constructs incrementally a pruning area using an interesting union-intersection property of dominance regions. Servers do not transmit points that fall within the pruning area in their local subspace. Our experiments confirm the effectiveness of the proposed methods under various settings.