  We describe analytical and numerical collisional evolution calculations for
the size distribution of icy bodies in the Kuiper Belt. For a wide range of
bulk properties, initial masses, and orbital parameters, our results yield
power-law cumulative size distributions, N_C propto r^{-q}, with q_L = 3.5 for
large bodies with radii of 10-100 km, and q_s = 2.5-3 for small bodies with
radii lesss than 0.1-1 km. The transition between the two power laws occurs at
a break radius of 1-30 km. The break radius is more sensitive to the initial
mass in the Kuiper Belt and the amount of stirring by Neptune than the bulk
properties of individual Kuiper Belt objects (KBOs). Comparisons with
observations indicate that most models can explain the observed sky surface
density of KBOs for red magnitudes, R = 22-27. For R < 22 and R > 28, the model
surface density is sensitive to the amount of stirring by Neptune, suggesting
that the size distribution of icy planets in the outer solar system provides
independent constraints on the formation of Neptune.
