  Given nontrivial finite groups $A$ and $B$, not both of order 2, we prove
that every finite simple group of sufficiently large rank is an image of the
free product $A \ast B$. To show this, we prove that every finite simple group
of sufficiently large rank is generated by a pair of subgroups isomorphic to
$A$ and $B$. This proves a conjecture of Tamburini and Wilson.
