  In this paper we focus on the uniqueness question for (expanding) solutions
of the Harmonic map flow coming out of smooth 0-homogeneous maps with values
into a closed Riemannian manifold. We introduce a relative entropy for two
purposes. On the one hand, we prove the existence of two expanding solutions
associated to any suitable solution coming out of a $0$-homogeneous map by a
blow-up and a blow-down process. On the other hand, generic uniqueness of
expanding solutions coming out of the same 0-homogeneous map of 0 relative
entropy is proved.
