The distribution of volcanic ash from the vent, and how it is deposited will depend on:
In general, the thickness of ash deposits decreases exponentially with increasing distance from a volcano. Secondary thickening may occur (as illustrated below) due to water and ash mixture clumping into larger particles in the ash clouds and then falling out due to a higher terminal velocity. On impact with the ground these clumps break, resulting in a thicker ash deposit (Brazier et al., 1983).
Once ash particles have been deposited on a surface, they will generally compact. The flatter the surface, the more efficient the compaction will be. The compaction may increase the bulk density of an ash deposit by as much as 50 percent, and slightly decrease the deposit thickness within a few weeks of an eruption.