  This work deals with the aggregation diffusion equation \[\partial_t \rho =
\Delta_p\rho + \lambda div((K_a*\rho)\rho),\] where $K_a(x)=\frac{x}{|x|^a}$ is
an attraction kernel and $\Delta_p$ is the so called $p$-Laplacian. We show
that the domain $a < p(d+1)-2d$ is subcritical with respect to the competition
between the aggregation and diffusion by proving that there is existence
unconditionally with respect to the mass. In the critical case we show
existence of solution in a small mass regime for an $L\ln L$ initial condition.
