  Let p be prime. We describe explicitly the resolution of singularities of
several families of wild Z/pZ-quotient singularities in dimension two,
including families that generalize the quotient singularities of type E_6, E_7,
and E_8 from p=2 to arbitrary characteristics. We prove that for odd primes,
any power of p can appear as the determinant of the intersection matrix of a
wild Z/pZ-quotient singularity. We also provide evidence towards the conjecture
that in this situation one may choose the wild action to be ramified precisely
at the origin.
