  We study the superconducting instabilities of a single species of
two-dimensional Rashba-Dirac fermions, as it pertains to the surface of a
three-dimensional time-reversal symmetric topological band insulators. We also
discuss the similarities as well as the differences between this problem and
that of superconductivity in two-dimensional time-reversal symmetric
noncentrosymmetric materials with spin-orbit interactions. The superconducting
order parameter has both s-wave and p-wave components, even when the
superconducting pair potential only transfers either pure singlets or pure
triplets pairs of electrons in and out of the condensate, a corollary to the
non-conservation of spin due to the spin-orbit coupling. We identify one single
superconducting regime in the case of superconductivity in the topological
surface states (Rashba-Dirac limit), irrespective of the relative strength
between singlet and triplet pair potentials. In contrast, in the Fermi limit
relevant to the noncentrosymmetric materials we find two regimes depending on
the value of the chemical potential and the relative strength between singlet
and triplet potentials. We construct explicitly the Majorana bound states in
these regimes. In the single regime for the case of the Rashba-Dirac limit,
there exist one and only one Majorana fermion bound to the core of an isolated
vortex. In the Fermi limit, there are always an even number (0 or 2 depending
on the regime) of Majorana fermions bound to the core of an isolated vortex. In
all cases, the vorticity required to bind Majorana fermions is unity, in
contrast to the half-flux in the case of two-dimensional $p_x \pm i p_y$
superconductors that break time-reversal symmetry.
