  We study conditions on a commutative ring R which are equivalent to the
following requirement; whenever X is a projective scheme over S = Spec(R) of
fiber dimension \leq d for some integer d \geq 0, there is a finite morphism
from X to P^d_S over S such that the pullbacks of coordinate hyperplanes give
prescribed subschemes of X provided these subschemes satisfy certain natural
conditions. We use our results to define a new kind of capacity for adelic
subsets of projective schemes X over global fields. This capacity can be used
to generalize the converse part of the Fekete-Szeg\H{o} Theorem.
