Final answer:
The axillary nerve is at the greatest risk during a posterior capsular release around the shoulder, as it is closely associated with the joint and innervates important shoulder muscles.
Step-by-step explanation:
The nerve at greatest risk during a posterior capsular release around the shoulder is the axillary nerve. This nerve runs closely to the shoulder joint and can be compromised during surgical procedures that address shoulder mobility issues, such as a posterior capsular release performed to treat conditions like adhesive capsulitis ("frozen shoulder"). It is critical during surgery to avoid damaging the axillary nerve, which innervates crucial shoulder muscles including the deltoid and teres minor, and provides sensory input to the skin covering the deltoid muscle.