  Streets and Tian introduced a parabolic flow of pluriclosed metrics. We
classify the long time behavior of homogeneous solutions of this flow on closed
complex surfaces including minimal Hopf, Inoue, Kodaira, and non-Kahler,
properly elliptic surfaces. We also construct expanding soliton solutions to
the flow on the universal covers of these surfaces by taking blowdown limits of
these homogeneous solutions.
