Study of Conformally Flat Initial Data for Highly Spinning Black Holes
  and their Early Evolutions
  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.
