  We study the effects of outflow/wind on the gravitational stability of
accretion discs around supermassive black holes using a set of analytical
steady-state solutions. Mass-loss rate by the outflow from the disc is assumed
to be a power-law of the radial distance and the amount of the energy and the
angular momentum which are carried away by the wind are parameterized
phenomenologically. We show that the mass of the first clumps at the
self-gravitating radius linearly decreases with the total mass-loss rate of the
outflow. Except for the case of small viscosity and high accretion rate,
generally, the self-gravitating radius increases as the amount of mass-loss by
the outflow increases. Our solutions show that as more angular momentum is lost
by the outflow, then reduction to the mass of the first clumps is more
significant.
