  We show, by comparing observations with theoretical models, that the observed
Kuiper Belt size distribution is well matched by coagulation models, which
start from an initial planetesimal population with radii of about 1km, and
subsequent collisional evolution. We find that the observed size distribution
for R > 30km has not been modified by collisional evolution over the age of the
solar system, and that the size distribution below R ~ 30km has been modified
by collisions and that its slope is well matched by collisional evolution
models that use published strength laws. We investigate in detail the resulting
size distribution of bodies ranging from 0.01km to 30km and find that its slope
changes several times as a function of radius before approaching the expected
value for an equilibrium collisional cascade of material strength dominated
bodies for R < 0.1km. Compared to a single power law size distribution that
would span the whole range from 0.01km to 30km, we find a strong deficit of
bodies around R ~10km and a strong excess of bodies around 2km. This deficit
and excess are caused by an excess mass in small planetesimals in the km size
range that was left over from the runaway growth phase and that leaves a
signature in the size distribution that is not erased after 4.5 Gyrs of
collisional evolution. Observations of the small KBO size distribution can
therefore test if large KBOs grew as a result of runaway growth and constrain
the initial planetesimal sizes. We find that results from recent KBO
occultation surveys and the observed KBO size distribution can be best matched
by an initial planetesimal population that contained about equal mass per
logarithmic mass bin in bodies ranging from 0.4km to 4km in radius. In
addition, we find that we cannot match the observed KBO size distribution if
most of the planetesimal mass was contained in bodies that were 10km in radius
or larger.
