  A universal coefficient theorem is proved for C*-algebras over an arbitrary
finite T_0-space X which have vanishing boundary maps. Under bootstrap
assumptions, this leads to a complete classification of unital/stable
real-rank-zero Kirchberg X-algebras with intermediate cancellation. Range
results are obtained for (unital) purely infinite graph C*-algebras with
intermediate cancellation and Cuntz-Krieger algebras with intermediate
cancellation. Permanence results for extensions of these classes follow.
