  We study similarity solutions to the multidimensional aggregation equation
$u_t+\Div(uv)=0$, $v=-\nabla K*u$ with general power-law kernels
$K(x)=|x|^\alpha,\alpha\in (2-d,2)$. We analyze the equation in different
regimes of the parameter $\alpha$. In the case when $\alpha\in [4-d,2)$, we
give a characterization all the "first kind" radially symmetric similarity
solutions. We prove that any such solution is a linear combination of a delta
ring and a delta mass at the origin. On the other hand, when $\alpha\in
(2-d,4-d)$, we show that there exist multi delta-ring similarity solutions in
$R^d$. In particular, our results imply that multi delta-ring similarity
solutions exist in 3D if $\alpha$ is just a little bit below 1.
