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We carry out global full magnetohydrodynamic simulations in axisymmetry, coupled with ray-tracing radiative transfer, consistent thermochemistry, and non-ideal MHD diffusivities. Magnetized models lacking EUV photons ($h\\nu>13.6\\ \\mathrm{eV}$) feature warm molecular outflows that have typical poloidal speeds $\\gtrsim 4\\ \\mathrm{km\\ s}^{-1}$. When the magnetization is sufficient to drive accretion rates $\\sim 10^{-8}\\ M_\\odot\\ \\mathrm{yr}^{-1}$, the wind mass-loss rate is comparable. 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