Dust in galaxies forms and evolves by various processes , and these dust processes change the grain size distribution and amount of dust in the interstellar medium ( ISM ) . 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 ( SNe II ) 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 , and this change occurs at earlier stage of galaxy evolution for a shorter star formation timescale ( for star formation time-scales = 0.5 , 5 and 50 Gyr , the change occurs about galactic age t \sim 0.6 , 2 and 5 Gyr , respectively ) . If we only take into account the processes which directly affect the total dust mass ( dust production by SNe II and AGB stars , dust destruction by SN shocks , and grain growth ) , the grain size distribution is biased to large grains ( a \sim 0.2 – 0.5 \mu m , where a is the grain radius ) . Therefore , shattering is crucial to produce small ( a \la 0.01 \mu m ) grains . 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 \sim 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 \sim 0.03 – 0.05 \mu m at t \sim 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 .