  We study noncentrosymmetric superconductors with the tetrahedral $T_d$,
tetragonal $C_{4v}$, and cubic point group $O$. The order parameter is computed
self-consistently in the bulk and near a surface for several different singlet
to triplet order parameter ratios. It is shown that a second phase transition
below $T_c$ is possible for certain parameter values. In order to determine the
surface orientation's effect on the order parameter suppression, the latter is
calculated for a range of different surface orientations. For selected
self-consistent order parameter profiles the surface density of states is
calculated showing intricate structure of the Andreev bound states (ABS) as
well as spin polarization. The topology's effect on the surface states and the
tunnel conductance is thoroughly investigated, and a topological phase diagram
is constructed for open and closed Fermi surfaces showing a sharp transition
between the two for the cubic point group $O$.
