Step 1: Idea:
Contrast the two mechanisms. $\text{S}_\text{N}1$: carbocation, polar protic solvent, tertiary substrate. $\text{S}_\text{N}2$: single step, strong nucleophile, small substrate, polar aprotic solvent.
Step 2: Result:
Only option C describes a feature that supports carbocation formation. A and D describe the $\text{S}_\text{N}2$ conditions, and B is the opposite of what ions need.
Final Answer:
Bulky alkyl groups on the carbon carrying the halogen favour $\text{S}_\text{N}1$, option (C).
\[ \boxed{\text{Bulky alkyl groups}} \]