**Core Concept**
Hemiplegia is a neurological condition characterized by paralysis or weakness on one side of the body, typically resulting from damage to the motor pathways in the brain. The most common cause of hemiplegia is a vascular event, such as a stroke, which disrupts blood flow to the brain.

**Why the Correct Answer is Right**
Thrombosis of a cerebral artery, particularly the middle cerebral artery (MCA), is the most common cause of hemiplegia. The MCA supplies a large portion of the brain's motor cortex, responsible for controlling voluntary movements. When a thrombus forms in the MCA, it can lead to ischemia and infarction of the surrounding brain tissue, resulting in hemiplegia. The MCA thrombosis typically affects the left hemisphere of the brain, leading to right-sided hemiplegia.

**Why Each Wrong Option is Incorrect**
* **Option A:** Thrombosis of the posterior cerebral artery (PCA) is less common and typically results in visual disturbances or posterior circulation strokes, rather than hemiplegia.
* **Option B:** Thrombosis of the anterior cerebral artery (ACA) can cause weakness or paralysis of the lower extremities, but is less likely to result in complete hemiplegia.
* **Option C:** Thrombosis of the vertebral artery can cause posterior circulation strokes, but is not a common cause of hemiplegia.

**Clinical Pearl / High-Yield Fact**
The "MCA syndrome" is a classic pattern of neurological deficits resulting from MCA thrombosis, characterized by contralateral hemiplegia, hemianesthesia, and visual field defects.

**Correct Answer:** C.