A pedagogical introduction to the classical hydrodynamic steady state solut
ions for flows in a spherically symmetric atmosphere is presented along wit
h a detailed analysis of the stability of such flows and a discussion of th
e Parker/Bondi phase diagram of solutions in the Mach number - stellar radi
us plane. This leads naturally to the scenario presented by Velli (1994) fo
r wind-accretion transitions, which helps to explain results from numerical
simulations in many contexts and gives a more comprehensive answer to the
question of why the solar wind and other steady state flows in spherical sy
metry must quite generally become supersonic.