  It has been suggested that a $\nu$p process can occur when hot, dense, and
proton-rich matter is expanding within a strong flux of anti-neutrinos. In such
an environment, proton-rich nuclides can be produced in sequences of proton
captures and (n,p) reactions, where the free neutrons are created in situ by
$\overline{\nu}_\mathrm{e}+\mathrm{p} \rightarrow \mathrm{n}+\mathrm{e}^+$
reactions. The detailed hydrodynamic evolution determines where the
nucleosynthesis path turns off from N = Z line and how far up the nuclear chart
it runs. In this work, the uncertainties on the final isotopic abundances
stemming from uncertainties in the nuclear reaction rates were investigated in
a large-scale Monte Carlo approach, simultaneously varying ten thousand
reactions. A large range of model conditions was investigated because a
definitive astrophysical site for the $\nu$p process has not yet been
identified. The present parameter study provides, for each model,
identification of the key nuclear reactions dominating the uncertainty for a
given nuclide abundance. As all rates appearing in the $\nu$p process involve
unstable nuclei, and thus only theoretical rates are available, the final
abundance uncertainties are larger than those for nucleosynthesis processes
closer to stability. Nevertheless, most uncertainties remain below a factor of
three in trajectories with robust nucleosynthesis. More extreme conditions
allow production of heavier nuclides but show larger uncertainties because of
the accumulation of the uncertainties in many rates and because the termination
of nucleosynthesis is not at equilibrium conditions. It is also found that the
solar ratio of the abundances of ${}^{92}$Mo and ${}^{94}$Mo could be
reproduced within uncertainties.
