Observations indicate that some extended outer disks have a sharp cutoff in the surface density of neutral hydrogen when this approaches the value of approximately 2 x 10(19) cm-2. In this paper we model these H I edges as places where the ratio of neutral to ionized hydrogen drops rapidly due to ionizing radiation. We use two different models for the vertical distribution of gas above the outer Galactic plane: in the first model we derive the density from the ideal gas law, while in the second model we insert a macroscopic pressure term and derive the density as for an isothermal slab. We consider two different sources of ionizing photons: external fluxes of different intensity and spectral index due to quasars, and a monochromatic UV flux due to neutrino decays inside and outside the disk. We find that galaxies which have a smaller gas scale height, because of a higher dark matter density or a larger external pressure, should show outer H i disks to a lower column density and smoother H I edges. The sharpness of the H I-H II transition and the total column density at which the medium is 50% ionized, are strongly correlated, irrespective of the gas or photon flux model used. We present several model fits to the H I sharp edge observed in the nearby galaxy M33. If today's UV background is dominated by attenuated quasar light and gives approximately 10(-14) H ionizations s-1, a large gas scale height or equivalently a nearly spherical halo is preferred. If ionizing photons from decaying neutrinos are responsible for the M33 sharp edge, then a thin outer H I disk, and consequently a flat dark matter halo, is required.