  The low accretion rate inferred for the GC source Sgr A* requires a distinct
type of accretion disk -- a starving disk. We investigate the structure of this
type of disk within the framework of thin Keplerian disk models taking into
account relativistic effects, detailed opacitiy tables and turbulent heat
transport. It appears as if starving disks are the perfect realization of
geometrically thin, optically thick disks with well behaved structure
functions. All in all starving disks are very stable structures with high
surface density, high optical depth and long viscous time scales. However,
S-curves in the Sigma-Mdot diagram occur, indicating a thermal limit-cycle
behaviour observable in the IR-NIR with timescales ranging between three years
and some thousand years. We propose that in Sgr A*, the main mass supply for
the disk might be a wind from the surrounding star cluster. As the disk is a
very stable and slowly evolving structure, it will inhibit spherical accretion
and incorporate the inflowing matter in the general accretion flow. The
situation in M31 may be very similar but with a more extreme set of parameters.
