We find a substantial class of pairs of *-homomorphisms between graph C*-algebras whose pullback C*-algebras are AF graph C*-algebras. As shown by a variety of examples from noncommutative topology, our result can be interpreted as a recipe for determining the quantum space obtained by shrinking a quantum subspace. This talk is devoted to explaining how to go beyond AF graph C*-algebras by considering extensions of graphs over sinks and proving an analogous theorem for the thus obtained graph C*-algebras. (Based on joint work with Alexandru Chirvasitu and Mariusz Tobolski.)