  In earlier work the authors proved the Bergman kernel expansion for
semipositive line bundles over a Riemann surface whose curvature vanishes to
atmost finite order at each point. Here we explore the related results and
consequences of the expansion in the semipositive case including: Tian's
approximation theorem for induced Fubini-Study metrics, leading order
asymptotics and composition for Toeplitz operators, asymptotics of zeroes for
random sections and the asymptotics of holomorphic torsion.
