**Core Concept**
In the context of hypoglossal nerve function, the motor innervation of the tongue is crucial for its movement. The hypoglossal nerve, the twelfth cranial nerve, is responsible for controlling the tongue's protrusion and retraction. The right hypoglossal nucleus is the location where the hypoglossal nerve originates in the brainstem.

**Why the Correct Answer is Right**
When the right hypoglossal nucleus is lesioned, the motor control of the right half of the tongue is compromised. As a result, during protrusion, the tip of the tongue will deviate towards the side of the lesion, which is the right side in this case. This is because the intact left hypoglossal nerve will pull the left half of the tongue forward, causing the right half to lag behind and deviate to the right. This phenomenon is known as "tongue deviation."

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the deviation of the tongue would be towards the left side, not the right side, if the left hypoglossal nucleus was lesioned.
* **Option B:** This option is incorrect because the deviation of the tongue would be towards the left side, not the right side, if the left hypoglossal nerve was damaged after it exits the brainstem.
* **Option D:** This option is incorrect because the deviation of the tongue would not be symmetrical, and the tip of the tongue would not end up in the midline.

**Clinical Pearl / High-Yield Fact**
In patients with a unilateral lesion of the hypoglossal nerve, the tongue will deviate towards the side of the lesion during protrusion. This is an important clinical sign that can help diagnose hypoglossal nerve damage.

**Correct Answer:** C.