In the scenario where plants have been tipped over, auxin will influence cell growth in the roots in the following way:
Auxin will build up on the lower side of the root and stimulate cell growth.
When a plant is tipped over, the gravity causes auxin to accumulate on the lower side of the root. This results in stimulated cell growth on that side, causing the root to bend downward toward the gravitational pull. The opposite side, having less auxin, will grow more slowly, resulting in this bending effect.