  Context. Current models of the size- and radial evolution of dust in
protoplanetary disks generally oversimplify either the radial evolution of the
disk (by focussing at one single radius or by using steady state disk models)
or they assume particle growth to proceed monodispersely or without
fragmentation. Further studies of protoplanetary disks - such as observations,
disk chemistry and structure calculations or planet population synthesis models
- depend on the distribution of dust as a function of grain size and radial
position in the disk.
  Aims. We attempt to improve upon current models to be able to investigate how
the initial conditions, the build-up phase, and the evolution of the
protoplanetary disk influence growth and transport of dust.
  Methods. We introduce a new version of the model of Brauer et al. (2008) in
which we now include the time-dependent viscous evolution of the gas disk, and
in which more advanced input physics and numerical integration methods are
implemented.
  Results. We show that grain properties, the gas pressure gradient, and the
amount of turbulence are much more influencing the evolution of dust than the
initial conditions or the build-up phase of the protoplanetary disk. We
quantify which conditions or environments are favorable for growth beyond the
meter size barrier. High gas surface densities or zonal flows may help to
overcome the problem of radial drift, however already a small amount of
turbulence poses a much stronger obstacle for grain growth.
