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Abstract To understand the mechanism behind high-zLyαnebulae, we simulate the scattering of Lyαin a Hihalo about a central Lyαsource. For the first time, we consider both smooth and clumpy distributions of halo gas, as well as a range of outflow speeds, total Hicolumn densities, Hispatial concentrations, and central source galaxies (e.g., with Lyαline widths corresponding to those typical of active galactic nucleus or star-forming galaxies). We compute the spatial-frequency diffusion and the polarization of the Lyαphotons scattered by atomic hydrogen. Our scattering-only model reproduces the typical size of Lyαnebulae (∼100 kpc) at total column densitiesN_{H I}≥ 10²⁰cm⁻²and predicts a range of positive, flat, and negative polarization radial gradients. We also find two general classes of Lyαnebula morphologies: with and without bright cores. Cores are seen whenN_{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 Lyαsurface brightness, spectral line shape, and polarization in the clumpy model with covering factorf_c≳ 5 approach those of the smooth model at the sameN_{H I}. A clumpy medium with highN_{H I}and lowf_c≲ 2 generates Lyαfeatures via scattering that the smooth model cannot: a bright core, symmetric line profile, and polarization jump.