- The primary role of the vasa vasorum in large blood vessels is to supply oxygen and nutrients to the vessel walls.
- Large arteries and veins have thick walls that are too extensive to be nourished solely by diffusion from the blood flowing within the lumen.
- Therefore, the vasa vasorum—small blood vessels located in the outer layers of the vessel wall (tunica adventitia and outer tunica media)—serve an essential function by penetrating these layers and providing the necessary oxygen and nutrients to maintain the health and integrity of the vessel tissue.

Key points to consider:
- The vessel walls of large arteries and veins are too thick for adequate diffusion alone.
- The vasa vasorum form a microvascular network supplying the outer part of the vessel wall.
- They are particularly important in the tunica adventitia and the outer part of the tunica media.
- Without the vasa vasorum, the cells in these layers would become ischemic and damaged.

Other options are incorrect because:
- Option 2: Venous return is facilitated mainly by valves and muscle contractions, not the vasa vasorum.
- Option 3: Transmission of nerve signals is primarily the function of the nervi vascularis, not the vasa vasorum.
- Option 4: Removal of waste from the vessel lumen is handled by the blood flow itself, not by the vasa vasorum.

Hence, the correct answer is Option 1: Supply oxygen and nutrients to the vessel walls.

Reference: Robbins Basic Pathology, 10th Edition, Chapter 10, Page 350