**Core Concept**
Voluntary movement of the eyeball is a complex process that involves the coordinated action of multiple cranial nerves and brainstem centers. The oculomotor nerve (CN III), trochlear nerve (CN IV), and abducens nerve (CN VI) are responsible for controlling the extraocular muscles, which enable movements of the eyeball.

**Why the Correct Answer is Right**
The correct answer is the oculomotor nerve (CN III), which is responsible for controlling the majority of the extraocular muscles, including the medial rectus, superior rectus, inferior rectus, and inferior oblique muscles. The oculomotor nerve also controls the levator palpebrae superioris muscle, which elevates the eyelid. The oculomotor nerve receives input from the frontal eye fields (FEF) and the superior colliculus in the brainstem, which are responsible for planning and executing voluntary eye movements. The oculomotor nerve then sends signals to the extraocular muscles via the oculomotor nerve nuclei in the brainstem.

**Why Each Wrong Option is Incorrect**
**Option A:** The trochlear nerve (CN IV) is responsible for controlling the superior oblique muscle, which is involved in rotational movements of the eyeball, but it is not responsible for voluntary movement of the eyeball.
**Option B:** The abducens nerve (CN VI) is responsible for controlling the lateral rectus muscle, which abducts the eyeball, but it is not responsible for controlling the majority of the extraocular muscles involved in voluntary eye movements.
**Option D:** The trigeminal nerve (CN V) is responsible for controlling facial sensation and motor functions, such as mastication, but it is not involved in the control of voluntary eye movements.

**Clinical Pearl / High-Yield Fact**
The oculomotor nerve (CN III) is often affected in conditions such as third nerve palsy, which can result in ptosis (drooping eyelid), diplopia (double vision), and limited eye movement.

**Correct Answer: C. Oculomotor nerve (CN III).**