  This paper considers a simple model in which dust produced in a planetesimal
belt migrates in toward the star due to P-R drag suffering destructive
collisions with other dust grains on the way. Assuming the dust is all of the
same size, the resulting surface density distribution can be derived
analytically and depends only on the parameter eta0=5000tau*sqrt(Mstar/r)/beta;
this parameter can be determined observationally with the hypothesis that
beta=0.5. For massive belts in which eta0>>1 dust is confined to the
planetesimal belt, while the surface density of more tenuous belts, in which
eta0<<1, is constant with distance from the star. The emission spectrum of dust
from planetesimal belts at different distances from different mass stars shows
that the dust belts which have been detected to date should have eta0>>1; dust
belts with eta0<<1 are hard to detect as they are much fainter than the stellar
photosphere. This is confirmed for a sample of 37 debris disk candidates for
which eta0 was determined to be >10. This means that these disks are so massive
that mutual collisions prevent dust from reaching the inner regions of these
systems and P-R drag can be ignored when studying their dynamics. Models for
the formation of structure in debris disks by the trapping of particles into
planetary resonances by P-R drag should be reconsidered. However, since
collisions do not halt 100% of the dust, this means that in the absence of
planetary companions debris disk systems should be populated by small
quantities of hot dust which may be detectable in the mid-IR. Even in disks
with eta0<<1 the temperature of dust emission is shown to be a reliable tracer
of the planetesimal distribution meaning that inner holes in the dust
distribution imply a lack of colliding planetesimals in the inner regions.
