The {\sc $k$-Circle Formation} problem asks a swarm of autonomous mobile robots to form disjoint circles. Each such circle is restricted to be centered at one of a number of pre-fixed points given in the plane. Each circle must contain exactly $k$ robots at distinct positions. The problem is studied in the Euclidean plane. The results of the paper are: \roster \item All the initial configurations and values of $k$ for which {\sc $k$-Circle Formation} is deterministically unsolvable are characterized. \item A deterministic distributed algorithm that solves the problem for the other initial configurations and values of $k$ is presented. \endroster