**Core Concept**
Hypersensitivity vasculitis, also known as leukocytoclastic vasculitis, is a type of inflammation of the blood vessels that is immune-mediated. It typically affects small blood vessels, and the underlying mechanism involves an abnormal immune response to various stimuli, such as infections, medications, or allergens.

**Why the Correct Answer is Right**
The correct answer is post-capillary venules because they are the primary sites of inflammation in hypersensitivity vasculitis. This is due to the fact that post-capillary venules are the sites of high permeability and have a high concentration of immune cells, such as neutrophils and macrophages. The inflammation in these vessels is characterized by the deposition of immune complexes, complement activation, and the release of various cytokines and chemokines, leading to the damage of the vascular endothelium.

**Why Each Wrong Option is Incorrect**
**Option A:** Capillaries are not typically involved in hypersensitivity vasculitis, as they are the smallest blood vessels and have a relatively low permeability compared to post-capillary venules.

**Option B:** Arterioles are also not typically involved in hypersensitivity vasculitis, as they are involved in the regulation of blood pressure and have a thicker muscular layer compared to post-capillary venules.

**Option D:** Medium-sized arteries are not typically involved in hypersensitivity vasculitis, as they are larger vessels that are more commonly affected by other types of vasculitis, such as Kawasaki disease or polyarteritis nodosa.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that hypersensitivity vasculitis typically affects the skin and kidneys, and the presence of purpura, palpable purpura, or renal involvement should raise suspicion for this condition. The diagnosis is often made based on clinical findings, laboratory tests, and biopsy results.

**✓ Correct Answer: C. Post-capillary venules**