We study conformally-flat initial data for an arbitrary number of spinning black holes with exact analytic solutions to the momentum constraints constructed from a linear combination of the classical Bowen-York and conformal Kerr extrinsic curvatures .
The solution leading to the largest intrinsic spin , relative to the ADM mass of the spacetime \epsilon _ { S } = S / M ^ { 2 } _ { ADM } , is a superposition with relative weights of \Lambda = 0.783 for conformal Kerr and ( 1 - \Lambda ) = 0.217 for Bowen-York .
In addition , we measure the spin relative to the initial horizon mass M _ { H _ { 0 } } , and find that the quantity \chi = S / M _ { H _ { 0 } } ^ { 2 } reaches a maximum of \chi ^ { max } = 0.9856 for \Lambda = 0.753 .
After equilibration , the final black-hole spin should lie in the interval 0.9324 < \chi _ { final } < 0.9856 .
We perform full numerical evolutions to compute the energy radiated and the final horizon mass and spin .
We find that the black hole settles to a final spin of \chi _ { final } ^ { max } = 0.935 when \Lambda = 0.783 .
We also study the evolution of the apparent horizon structure of this maximal black hole in detail .