  We examine the flow from asymptotic giant branch (AGB) stars when along a
small solid angle the optical depth due to dust is very large. We consider two
types of flows. In the first, small cool spots are formed on the surface of
slowly rotating AGB stars. During the last AGB phase when mass loss rate is
high, the dust shields the region above it from the stellar radiation. This
leads to both further dust formation in the shaded region, and the convergence
of the stream toward the shaded region. A concentration of magnetic cool spots
toward the equator will lead to a density contrast of up to a few between the
equatorial and polar directions. This process can explain the positive
correlation between high mass loss rate and a larger departure from sphericity
in progenitors of elliptical planetary nebulae. In the second type of flow, the
high density in the equatorial plane is formed by a binary interaction, where
the secondary star is close to, but outside the AGB envelope. The shielding of
the radiation by dust results in a very slow and dense flow in the equatorial
plane. We suggest this flow as an alternative explanation for the equatorial
dense matter found at several hundred astronomical units around several
post-AGB binary systems.
