  We construct a dust evolution model taking into account the grain size
distribution, and investigate what kind of dust processes determine the grain
size distribution at each stage of galaxy evolution. In addition to the dust
production by type II supernovae (SNeII) and asymptotic giant branch (AGB)
stars, we consider three processes in the ISM: (i) dust destruction by SN
shocks, (ii) metal accretion onto the surface of preexisting grains in the cold
neutral medium (CNM) (called grain growth), and (iii) grain-grain collisions
(shattering and coagulation) in the warm neutral medium (WNM) and CNM. We found
that the grain size distribution in galaxies is controlled by stellar sources
in the early stage of galaxy evolution, and that afterwards the main processes
that govern the size distribution changes to those in the ISM. Since shattering
produces a large abundance of small grains (consequently, the surface-to-volume
ratio of grains increases), it enhances the efficiency of grain growth,
contributing to the significant increase of the total dust mass. Grain growth
creates a large bump in the grain size distribution around a ~ 0.01 \mu m.
Coagulation occurs effectively after the number of small grains is enhanced by
shattering, and the grain size distribution is deformed to have a bump at a ~
0.03 - 0.05 \mu m at t ~ 10 Gyr. We conclude that the evolutions of the total
dust mass and the grain size distribution in galaxies are closely related to
each other, and the grain size distribution changes considerably through the
galaxy evolution because the dominant dust processes which regulate the grain
size distribution change.
