Which nerve is not part of the axillary nerve branches?

The ulnar nerve is not part of the axillary nerve branches. The axillary nerve primarily innervates the deltoid and teres minor muscles, as well as providing sensation to the skin overlying the lateral aspect of the shoulder. It does so through its own branches, which include the circumflex humeral artery.

On the other hand, the radial, musculocutaneous, and median nerves are all branches of the brachial plexus but serve different functions and anatomical areas. The radial nerve, for example, innervates the posterior compartment of the arm and forearm, while the musculocutaneous nerve innervates the flexor muscles of the arm. The median nerve primarily controls muscles of the forearm and hand. Since the ulnar nerve has a distinct pathway and innervation that does not overlap with the axillary nerve's distribution, it is the correct choice in this context.