We use elementary algebraic methods to reprove a theorem which was proved by Pop using rigid analytic geometry and in a less general form by Harbater using formal algebraic patching:

Let $C$ be an algebraically closed field of cardinality $m$. Consider a subset $S$ of $\bbP^1(C)$ of cardinality $m$. Then the fundamental group of $\bbP^1(C)\hefresh S$ is isomorphic to the free profinite group of rank $m$.

We also observe that if $\chr(C)\ne0$ and $0<\card(S)<m$, then $\pi_1(\bbP^1(C)\hefresh S)$ is not isomorphic to a free profinite group.