  The accretion process onto a magnetized isolated neutron star, which captures
material from the interstellar medium, is discussed. The evolutionary track of
such a star can be presented as a sequence of four states: ejector, supersonic
propeller, subsonic propeller, and steady accretor. I show that subsonic
propeller - accretor transition does not occur as long as the magnetic field of
the star is strong enough to control the accretion flow in the stellar
vicinity. During the subsonic propeller state the accretion rate onto the
stellar surface is limited to the rate of plasma diffusion into its
magnetosphere. The diffusion rate is at least three orders of magnitude smaller
than the maximum possible mass capture rate by the star. Therefore, the
expected accretion luminosity of magnetized isolated neutron stars is at least
three orders of magnitude smaller than that previously evaluated.
