Let $X\to \mathbf{P}^1$ be a branched cover of the complex projective line, where $X$ is a compact connected Riemann surface. Let $G=\mathrm{Aut}(Y/\mathbf{P}^1)$.
Question 1. Could somebody provide some examples of branched covers $X\to \mathbf{P}^1$ for which $G= (0)$?
One could construct a compact connected Riemann surface without automorphisms to this end.