Gas overdensity in our standard simulation BHs5e0.1v5 at six cosmic epochs z = 3, 2, 1, 0.5, 0.2, 0. The BH that would become most massive at z = 0 is backtracked, and each panel shows a projected (2000 h⁻¹ kpc)³ comoving volume around the location of this BH. The red cross symbols indicate the positions of all the BHs inside the plotted region, where the symbol size is proportional to BH mass. The black circle is the virial radius, R_200, of the host galaxy of the backtracked BH, the red circles depict the R₂₀₀ of galaxies with the mass range M_halo > 10¹² M_⊙, and the blue circles show the R₂₀₀ of (10¹¹ < M_halo < 10¹²) M_⊙ galaxies.