In this paper, we consider the problem of allocating a large number of independent, equal-sized tasks to a heterogeneous "grid" computing platform. We use a non-oriented graph to model a grid, where resources can have different speeds of computation and communication, as well as different overlap capabilities. We show how to determine the optimal steady-state scheduling strategy for each processor. Because spanning trees are easier to deal with in practice, a natural question arises: how to extract the best spanning tree, i.e. the one with optimal steady-state throughput, out of a general interconnection graph? We show that this problem is NP-Complete. Still, we introduce and compare several low-complexity heuristics to determine a sub-optimal spanning tree.