  In this paper, we establish the asymptotic expansion at infinity of gradient
graph in dimension 2 with vanishing mean curvature at infinity. This
corresponds to our previous results in higher dimensions and generalizes the
results for minimal gradient graph on exterior domain in dimension 2. Different
from the strategies for higher dimensions, instead of the equivalence of
Green's function on unbounded domains, we apply a version of iteration methods
from Bao--Li--Zhang [Calc.Var PDE, 52(2015), pp. 39-63] that is refined by
spherical harmonic expansions to provide a more explicit asymptotic behavior
than known results.
