  Stationary axisymmetric binary systems of unequal co and counter-rotating
extreme Kerr black holes apart by a conical singularity are studied. Both
solutions are well identified as two $3$-parametric subfamilies of the
Kinnersley-Chitre metric, and fully depicted by Komar parameters: the two
masses $M_{1}$ and $M_{2}$, and a coordinate distance $R$, where the angular
momenta $J_{1}$ and $J_{2}$ are functions of these parameters. Our physical
representation allows us to identify some limits and novel physical properties.
