  Decretion (or external) disks are gas disks freely expanding to large radii
due to their internal stresses. They are expected to naturally arise in tidal
disruption events, around Be stars, in mass-losing post main sequence binaries,
as a result of supernova fallback, etc. Their evolution is theoretically
understood in two regimes: when the central object does not exert torque on the
disk (a standard assumption for conventional accretion disks) or when no mass
inflow (or outflow) occurs at the disk center. However, many astrophysical
objects - circumbinary disks, Be stars, neutron stars accreting in a propeller
regime, etc. - feature non-zero torque simultaneously with the non-zero
accretion (or ejection of mass) at the disk center. We provide a general
description for the evolution of such disks (both linear and non-linear) in the
self-similar regime, to which the disk should asymptotically converge with
time. We identify a similarity parameter $\lambda$, which is uniquely related
to the degree, to which the central mass accretion is suppressed by the
non-zero central torque. The known decretion disk solutions correspond to the
two discrete values of $\lambda$, while our new solutions cover a continuum of
its physically allowed values, corresponding to either accretion or mass
ejection by the central object. A direct relationship between $\lambda$ and
central $\dot M$ and torque is also established. We describe the time evolution
of the various disk characteristics for different $\lambda$, and show that the
observable properties (spectrum and luminosity evolution) of the decretion
disks are in general different from the standard accretion disks with no
central torque.
