abc estimate, integral points, and geometry of P^ n minus hyperplanes

Let K be a field and H be a set of hyperplanes in P n (K). When K is a function field, we show that the following are equivalent. (a) H is nondegenerate over K. (b) The height of the (S, H)-integral points of P n (K) -H is bounded. (c) P n K -H is an abc variety. When K is a number field and H is nondegenerate over K, we establish an explicit bound on the number of (S, H)-integral points of P n (K) -H. Finally, we discuss the geometric properties of holomorphic maps into P n (C) omitting a set of hyperplanes with moving targets.