  Context. Grains in circumstellar disks are believed to grow by mutual
collisions and subsequent sticking due to surface forces. Results of many
fields of research involving circumstellar disks, such as radiative transfer
calculations, disk chemistry, magneto-hydrodynamic simulations largely depend
on the unknown grain size distribution.
  Aims. As detailed calculations of grain growth and fragmentation are both
numerically challenging and computationally expensive, we aim to find simple
recipes and analytical solutions for the grain size distribution in
circumstellar disks for a scenario in which grain growth is limited by
fragmentation and radial drift can be neglected.
  Methods. We generalize previous analytical work on self-similar steady-state
grain distributions. Numerical simulations are carried out to identify under
which conditions the grain size distributions can be understood in terms of a
combination of power-law distributions. A physically motivated fitting formula
for grain size distributions is derived using our analytical predictions and
numerical simulations.
  Results. We find good agreement between analytical results and numerical
solutions of the Smoluchowski equation for simple shapes of the kernel
function. The results for more complicated and realistic cases can be fitted
with a physically motivated "black box" recipe presented in this paper. Our
results show that the shape of the dust distribution is mostly dominated by the
gas surface density (not the dust-to-gas ratio), the turbulence strength and
the temperature and does not obey an MRN type distribution.
