  For any $n>1$, we construct examples branched Galois coverings from $M$ to
the nth projective space ${\mathbb P}^n$ where $M$ is one of $({\mathbb
P}^1)^n$, ${\mathbb C}^n$ or $(B_1)^n$, and $B_1$ is the 1-ball. In terms of
orbifolds, this amounts to giving examples of orbifolds over ${\mathbb P}^n$
uniformized by $M$.We also discuss the related "orbifold braid groups".
