  We solve the 1D neutrino-heated non-relativistic MHD wind problem for
conditions that range from slowly rotating (spin period P > 10 ms) protoneutron
stars (PNSs) with surface field strengths typical of radio pulsars (B < 10^13
G), to "proto-magnetars" with B ~ 10^14-10^15 G in their hypothesized rapidly
rotating initial states (P ~ 1 ms). We use the simulations of Bucciantini et
al. (2006) to map our monopole results onto a more physical dipole geometry and
to estimate the spindown of PNSs when their winds are relativistic. We then
quantify the effects of rotation and magnetic fields on the mass loss, energy
loss, and r-process nucleosynthesis in PNS winds. We describe the evolution of
PNS winds through the Kelvin-Helmholtz cooling epoch, emphasizing the
transition between (1) thermal neutrino-driven, (2) non-relativistic
magnetically-dominated, and (3) relativistic magnetically-dominated outflows.
We find that proto-magnetars with P ~ 1 ms and B > 10^15 G drive relativistic
winds with luminosities, energies, and Lorentz factors (magnetization sigma ~
0.1-1000) consistent with those required to produce long duration gamma-ray
bursts and hyper-energetic supernovae (SNe). A significant fraction of the
rotational energy may be extracted in only a few seconds, sufficiently rapidly
to alter the asymptotic energy of the SN remnant, its morphology, and,
potentially, its nucleosynthetic yield. Winds from PNSs with more modest
rotation periods (2 - 10 ms) and with magnetar-strength fields produce
conditions significantly more favorable for the r-process than winds from
slowly rotating PNSs. Lastly, we show that energy and momentum deposition by
convectively-excited waves further increase the likelihood of successful
r-process in PNS winds.
