I know that, according to the Riemann mapping theorem, for any non-empty simply connected open subset $U$ of the complex plane $\mathbb{C}$ which is not all of $\mathbb{C}$, then there exists a conformal map from $U$ onto the open unit disk.
I am wondering if it possible to find conformal (or quasi-conformal) maps between regions having different numbers of holes. For example: between an annulus (which is doubly connected) and a square (which is simply connected).