Step 1: Understanding the Concept:
The \(\text{S}_\text{N}1\) reaction is a two step reaction. The slow step is the loss of the leaving group to give a carbocation. Anything that stabilises this carbocation favours \(\text{S}_\text{N}1\).
Step 2: Check each option:
A: A strong nucleophile favours \(\text{S}_\text{N}2\), since the nucleophile takes part in the rate step. In \(\text{S}_\text{N}1\) it does not matter. So A is wrong.
B: \(\text{S}_\text{N}1\) forms ions, which need a polar protic solvent to stabilise them. A non-polar solvent is wrong.
C: Bulky alkyl groups (as in tertiary halides) give a stable tertiary carbocation through the \(+I\) effect and hyperconjugation. This favours \(\text{S}_\text{N}1\). It is correct.
D: Small alkyl groups (methyl, primary) form unstable carbocations and are open to back-side attack, so they favour \(\text{S}_\text{N}2\).
Final Answer:
Bulky alkyl groups on the carbon carrying the halogen favour \(\text{S}_\text{N}1\), option (C).
\[ \boxed{\text{Bulky alkyl groups}} \]