Which nerve is associated with the structures found in the quadrilateral space?

The axillary nerve is the correct choice as it innervates the deltoid and teres minor muscles, both of which are located in the shoulder region, specifically associated with the quadrilateral space. This anatomical space, also known as the quadrangular space, is bounded by the teres minor and teres major muscles, the long head of the triceps, and the surgical neck of the humerus. The axillary nerve passes through this space alongside the posterior circumflex humeral artery, making it integral to the nerve's function in providing motor innervation.

Understanding the role of the axillary nerve is crucial in assessing injuries in this area, especially in cases such as shoulder dislocations or fractures around the humeral neck, which can lead to damage of the axillary nerve. This can result in symptoms like weakness in arm abduction and numbness over the lateral shoulder, indicating the importance of the nerve's anatomical location and function related to the structures of the quadrilateral space. The other nerves listed, while having their own roles in upper extremity function, do not pass through the quadrilateral space or have direct associations with the structures therein.