  We show that small solids in low mass, turbulent protoplanetary disks collect
into self-gravitating rings. Growth is faster than disk lifetimes and radial
drift times for moderately strong turbulence, characterized by dimensionless
diffusivities, $\alpha_g < 10^{-6} -- 10^{-3}$ when particles are mm-sized.
This range reflects a strong dependance on disk models. Growth is faster for
higher particle surface densities. Lower gas densities and larger solids also
give faster growth, as long as aerodynamic coupling is tight. In simple power
law models, growth is slowest around ~0.3 AU, where drag coupling is strongest
for mm-sized solids. Growth is much faster close to the star where orbital
times are short, with implications for in situ formation of short period
extrasolar planets. Growth times also decrease toward the outer disk where
lower gas densities allow greater particle settling. Beyond roughly Kuiper Belt
distances however, solids are sufficiently decoupled from gas that dissipative
gravitational instabilities are less effective. Turbulence not only slows
growth, but also increases radial wavelengths. The initial solid mass in an
unstable ring can be ~0.01 M_Earth or greater, huge compared to km-sized
planetesimals. Nonlinear fragmentation, which has not been studied in detail,
will lower the final planetesimal mass. We consider applications to the
asteroid belt and discuss the alternate hypothesis of collisional
agglomeration.
