  Though widely observed to be emanating from a variety of astrophysical
sources, the underlying physical mechanism behind the formation of galactic and
extragalactic outflows is still enshrouded in a veil of mystery. In addition,
it has not been possible to calculate accurately the amount of matter expelled
in these events. In this article we present a {\em non-self-similar analytical
model}, which, for the first time, we believe is able to explain the outflow
formation phenomenon as well as compute the mass outflow rate by simultaneously
solving the equations governing the exact transonic accretion and outflow. Our
model predicts the dependence of this rate on various flow parameters as well
as the {\em exact} location from where the outflows are launched.
