  We analyze the general structure of soft scalar masses emerging in
superstring models involving anomalous U(1) symmetries, with the aim of
characterizing more systematically the circumstances under which they can
happen to be flavor universal. We consider both heterotic orbifold and
intersecting brane models, possibly with several anomalous and non-anomalous
spontaneously broken U(1) symmetries. The hidden sector is assumed to consist
of the universal dilaton, Kahler class and complex structure moduli, which are
supposed to break supersymmetry, and a minimal set of Higgs fields which
compensate the Fayet-Iliopoulos terms. We leave the superpotential that is
supposed to stabilize the hidden sector fields unspecified, but we carefully
take into account the relations implied by gauge invariance and the constraints
required for the existence of a metastable vacuum with vanishing cosmological
constant. The results are parametrized in terms of a constrained Goldstino
direction, suitably defined effective modular weights, and the U(1) charges and
shifts. We show that the effect induced by vector multiplets strongly depends
on the functional form of the Kahler potential for the Higgs fields. We find in
particular that whenever these are charged matter fields, like in heterotic
models, the effect is non-trivial, whereas when they are shifting moduli
fields, like in certain intersecting brane models, the effect may vanish.
