**Core Concept**
The question assesses the pharmacokinetics of non-depolarizing muscle relaxants, specifically their excretion pathways. Non-depolarizing muscle relaxants are a class of medications used to facilitate endotracheal intubation and provide muscle relaxation during surgery.

**Why the Correct Answer is Right**
The correct answer is Vecuronium. Vecuronium is primarily excreted through the kidneys, with approximately 75% of the drug eliminated unchanged in the urine. This is due to its low lipid solubility and high water solubility, which allows for efficient renal excretion. Vecuronium is also metabolized to a lesser extent by the liver, but renal excretion is the primary route of elimination.

**Why Each Wrong Option is Incorrect**
**Option A:** Atracurium - Atracurium is primarily metabolized by Hofmann elimination, a chemical process that occurs in plasma, rather than being excreted through the kidneys.
**Option B:** Pancuronium - Pancuronium is excreted mainly through the liver, with some renal excretion, but not to the same extent as Vecuronium.
**Option C:** Rocuronium - Rocuronium is primarily excreted through the liver and bile, rather than the kidneys.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that non-depolarizing muscle relaxants have varying pharmacokinetic profiles, which can affect their duration of action and elimination. Vecuronium's high renal excretion makes it a suitable choice for patients with liver dysfunction or those requiring prolonged muscle relaxation.

**Correct Answer:** C. Vecuronium