  We consider the fractional mean curvature flow of entire Lipschitz graphs. We
provide regularity results, and we study the long time asymptotics of the flow.
In particular we show that in a suitable rescaled framework, if the initial
graph is a sublinear perturbation of a cone, the evolution asymptotically
approaches an expanding self-similar solution. We also prove stability of
hyperplanes and of convex cones in the unrescaled setting.
