What system carries auxin to move to the darker side?

Vascular system.

Phototropisms are caused by an unequal distribution of auxin. This makes the plant grow either towards or away from the light, depending on which part of the plant receives the light.

In a stem, the cells on the shaded side contain more auxin and grow longer than the cells on the light side. This causes the stem to grow towards the light. It is vital to note that the plant does NOT bend towards the light.

some fungi obtain their nutrients from a living host (plant or animal) and are called most biotrophic fungi have fairly narrow host ranges—they are specialized on a limited called rhizomorphs that allow the fungus to grow from one tree to another. ascospores are formed inside a sac-like structure called an ascus. so your answer is a