Fraction of intrinsic TNG100 LAEs relative to the total galaxy population, for the three redshifts: z = 2.4 (blue), z = 3.1 (magenta), and z = 4.5 (green). The LAE sample represents the intrinsic LAE population, not affected by our stochastic selection. Upper panel: Fraction of total LAEs relative to the total galaxy population as a function of different properties. Left: as a function of the halo mass, M₂₀₀. Middle: dependence with stellar mass, M_*. Right: as a function of the star formation rate (SFR). Shaded regions correspond to uncertainties, which were estimated based on the dispersion and by assuming Poisson errors. The trends indicate that LAEs preferentially reside in intermediate-mass halos, with moderate stellar masses and SFR, showing a consistent behavior across redshifts. Bottom panel: Same as the upper panel, but showing the fraction of LAEs separated into central galaxies (defined as those with the highest stellar mass within a halo, dotted lines) and satellite galaxies (dashed lines), relative to the total galaxy population in TNG100.