  We explore the properties of cold gravitoturbulent accretion disks -
non-fragmenting disks hovering on the verge of gravitational instability -
using a realistic prescription for the effective viscosity caused by
gravitational torques. This prescription is based on a direct relationship
between the angular momentum transport in a thin accretion disk and the disk
cooling in a steady state. Assuming that opacity is dominated by dust we are
able to self-consistently derive disk properties for a given $\dot M$ assuming
marginal gravitational stability. We also allow external irradiation of the
disk and account for a non-zero background viscosity which can be due to the
MRI. Spatial transitions between different co-existing disk states (e.g.
between irradiated and self-luminous or between gravitoturbulent and viscous)
are described and the location of the boundary at which disk must fragment is
determined in a variety of situations. We demonstrate in particular that at low
enough $\dot M$ external irradiation stabilizes gravitoturbulent disk against
fragmentation all the way to infinity thus providing means of steady mass
transport to the central object. Implications of our results for the
possibility of planet formation by gravitational instability in protoplanetary
disks and star formation in the Galactic Center and for the problem of feeding
supermassive black holes in galactic nuclei are discussed.
