  Let Y be a noncompact rank one locally symmetric space of finite volume. Then
Y has a finite number e(Y) > 0 of topological ends. In this paper, we show that
for any natural number n, the Y with e(Y) \leq n that are arithmetic fall into
finitely many commensurability classes. In particular, there is a constant c_n
such that n-cusped arithmetic orbifolds do not exist in dimension greater than
c_n. We make this explicit for one-cusped arithmetic hyperbolic n-orbifolds and
prove that none exist for n \geq 30.
