  We examine how the uncertainties involved in supernova dynamics as well as in
nuclear data inputs affect the nup-process in the neutrino-driven winds. For
the supernova dynamics, we find that the wind termination by the preceding
dense ejecta shell, as well as the electron fraction (Y_{e, 3}; at 3 10^9 K)
play a crucial role. A wind termination within the temperature range of (1.5-3)
10^9 K greatly enhances the efficiency of the nu p-process. This implies that
the early wind phase, when the innermost layer of the preceding supernova
ejecta is still 200-1000 km from the center, is most relevant to the
nup-process. The outflows with Y_{e, 3} = 0.52-0.60 result in the production of
the p-nuclei up to A=108 with interesting amounts. Furthermore, the p-nuclei up
to A=152 can be produced if Y_{e, 3} = 0.65 is achieved. For the nuclear data
inputs, we test the sensitivity to the rates relevant to the breakout from the
pp-chain region (A < 12), to the (n, p) rates on heavy nuclei, and to the
nuclear masses along the nup-process pathway. We find that a small variation of
the rates of triple-alpha and of the (n, p) reaction on 56Ni leads to a
substantial change in the p-nuclei production. We also find that 96Pd (N=50) on
the nup-process path plays a role as a second seed nucleus for the production
of heavier p-nuclei. The uncertainty in the nuclear mass of 82Zr can lead to a
factor of two reduction in the abundance of the p-isotope 84Sr.
