**Core Concept**
The external urethral sphincter plays a crucial role in maintaining urinary continence. Its function is primarily controlled by the autonomic nervous system, specifically the sympathetic and parasympathetic branches, which regulate the contraction and relaxation of the sphincter muscle.

**Why the Correct Answer is Right**
The external urethral sphincter is innervated by the **pudendal nerve**. During a radical prostatectomy, the surgeon must be cautious not to damage the nerves surrounding the prostate gland, including the pudendal nerve. Injury to the pudendal nerve can lead to paralysis of the external urethral sphincter, resulting in urinary incontinence. The pudendal nerve arises from the S2-S4 nerve roots and provides motor innervation to the external urethral sphincter, as well as sensory innervation to the perineal region.

**Why Each Wrong Option is Incorrect**
**Option A:** The **ilioinguinal nerve** primarily provides sensory innervation to the inguinal region and does not control the external urethral sphincter.
**Option B:** The **obturator nerve** innervates the adductor muscles of the thigh and is not involved in the control of the external urethral sphincter.
**Option C:** The **hypogastric nerve** is a sympathetic nerve that provides innervation to the pelvic organs, but it does not directly control the external urethral sphincter.

**Clinical Pearl / High-Yield Fact**
It's essential to note that the **nerve-sparing technique** is often employed during radical prostatectomy to minimize damage to the surrounding nerves, including the pudendal nerve. This technique can help preserve urinary continence and erectile function in patients undergoing prostate cancer surgery.

**Correct Answer:** D. Pudendal nerve.