  We consider an aggregation-diffusion model, where the diffusion is nonlinear
of porous medium type and the aggregation is governed by the Riesz potential of
order s. The addition of a quadratic diffusion term produces a more precise
competition with the aggregation term for small s, as they have the same
scaling if s=0. We prove existence and uniqueness of stationary states and we
characterize their asymptotic behavior as s goes to zero. Moreover, we prove
existence of gradient flow solutions to the evolution problem by applying the
JKO scheme.
