We use N-body simulations on highly parallel supercomputers to study the structure of Galactic dark matter halos. The systems form by gravitational collapse from scale-free and more general Gaussian initial density perturbations in an expanding 400 Mpc 3 spherical slice of an Einstein-deSitter universe. We use N∼10 6 and a force softening e=5 kpc in most of our models. We analyze the structure and kinematics of the ∼10 2 largest relaxed halos in each of 10 separate simulations