**Core Concept**
The parietal branch of the middle meningeal artery is closely related to the cerebrum, specifically supplying blood to the dura mater covering the cerebral cortex. Its involvement can lead to complications due to its proximity to vital structures.

**Why the Correct Answer is Right**
The parietal branch of the middle meningeal artery runs between the dura mater and the inner table of the skull, close to the temporal bone. Its involvement can lead to damage to the structures within the temporal bone, including the cochlear nerve, which is responsible for hearing. This results in contralateral deafness because the cochlear nerve crosses over to the opposite side of the brainstem, where it synapses with the auditory cortex. This crossing occurs at the level of the cochlear nuclei in the pons.

**Why Each Wrong Option is Incorrect**
**Option A:** Hemiplagia of the contralateral side is incorrect because the parietal branch of the middle meningeal artery is not directly related to the motor or sensory pathways that control the contralateral side of the body. Damage to this artery would not directly affect motor or sensory function on the opposite side of the body.

**Option B:** Ipsilateral deafness is incorrect because the cochlear nerve crosses over at the level of the cochlear nuclei in the pons, resulting in contralateral deafness, not ipsilateral deafness.

**Option D:** All of the above is incorrect because only contralateral deafness is a direct consequence of parietal branch of the middle meningeal artery involvement.

**Clinical Pearl / High-Yield Fact**
The middle meningeal artery is a key landmark in neurosurgical procedures, particularly in the management of epidural hematomas. Its anatomy and course should be well understood by neurosurgeons and neurologists to avoid complications.

**✓ Correct Answer: C. Contalateral deafness**