Final answer:
The spinal accessory nerve exits the cranium through the jugular foramen, which also facilitates the passage of venous return blood from the brain.
Step-by-step explanation:
The spinal accessory nerve, also known as the eleventh cranial nerve, is responsible for the contraction of neck muscles, specifically the sternocleidomastoid and trapezius muscles. This nerve exits the cranium through the jugular foramen, which is situated immediately inferior to the internal acoustic meatus and is an irregularly shaped large opening through the base of the skull. This foramen not only allows passage for the spinal accessory nerve but is also the exit point for venous return blood leaving the brain.