Abstract To understand the mechanism behind high- z Ly α nebulae, we simulate the scattering of Ly α in a H i halo about a central Ly α source. For the first time, we consider both smooth and clumpy distributions of halo gas, as well as a range of outflow speeds, total H i column densities, H i spatial concentrations, and central source galaxies (e.g., with Ly α line widths corresponding to those typical of active galactic nucleus or star-forming galaxies). We compute the spatial-frequency diffusion and the polarization of the Ly α photons scattered by atomic hydrogen. Our scattering-only model reproduces the typical size of Ly α nebulae (∼100 kpc) at total column densities N H I ≥ 10 20 cm −2 and predicts a range of positive, flat, and negative polarization radial gradients. We also find two general classes of Ly α nebula morphologies: with and without bright cores. Cores are seen when N H I is low, i.e., when the central source is directly visible, and are associated with a polarization jump, a steep increase in the polarization radial profile just outside the halo center. Of all the parameters tested in our smooth or clumpy medium model, N H I dominates the trends. The radial behaviors of the Ly α surface brightness, spectral line shape, and polarization in the clumpy model with covering factor f c ≳ 5 approach those of the smooth model at the same N H I . A clumpy medium with high N H I and low f c ≲ 2 generates Ly α features via scattering that the smooth model cannot: a bright core, symmetric line profile, and polarization jump.