  We study properties of dark matter halos at high redshifts z=2-10 for a vast
range of masses with the emphasis on dwarf halos with masses 10^7-10^9 Msun/h.
We find that the density profiles of relaxed dwarf halos are well fitted by the
NFW profile and do not have cores. We compute the halo mass function and the
halo spin parameter distribution and find that the former is very well
reproduced by the Sheth & Tormen model while the latter is well fitted by a
lognormal distribution with lambda_0 = 0.042 and sigma_lambda = 0.63. We
estimate the distribution of concentrations for halos in mass range that covers
six orders of magnitude from 10^7 Msun/h to 10^13} Msun/h, and find that the
data are well reproduced by the model of Bullock et al. The extrapolation of
our results to z = 0 predicts that present-day isolated dwarf halos should have
a very large median concentration of ~ 35. We measure the subhalo circular
velocity functions for halos with masses that range from 4.6 x 10^9 Msun/h to
10^13 Msun/h and find that they are similar when normalized to the circular
velocity of the parent halo. Dwarf halos studied in this paper are many orders
of magnitude smaller than well-studied cluster- and Milky Way-sized halos. Yet,
in all respects the dwarfs are just down-scaled versions of the large halos.
They are cuspy and, as expected, more concentrated. They have the same spin
parameter distribution and follow the same mass function that was measured for
large halos.
