Approximating list-coloring on a fixed surface

It is well-known that approximating the chromatic number within a factor of n(1-epsilon) cannot be done in polynomial time for any epsilon > 0; unless coRP = NP. Also, it is known that computing the list-chromatic number is much harder than the chromatic number (assuming that the complexity classes NP and coNP are different). In fact, the problem of deciding if a given graph is f-list-colorable for a function f : V -> {k - 1, k} for k >= 3 is pi(p)(2)-complete.