  We revisit Kesten's argument for the upper bound on the growth rate of DLA.
We are able to make the argument robust enough so that it applies to many
graphs, where only control of the heat kernel is required. We apply this to
many examples including transitive graphs of polynomial growth, graphs of
exponential growth, non-amenable graphs, super-critical percolation on Z^d,
high dimensional pre-Sierpinski carpets. We also observe that a careful
analysis shows that Kesten's original bound on Z^3 can be improved from t^{2/3}
to (t log t)^{1/2} .
