Methodology followed in DECODE to form and evolve galaxies and supermassive black holes. The SFR-HAR relation, computed via abundance matching, is used to assign galaxies following the accretion histories of their host dark matter haloes. Observationally determined sBHAR distributions at each redshift are used to assign the accretion rates to the central SMBHs following the stellar mass growths of their host galaxies. Black hole accretion and star formation rate are halted using empirically inferred M_BH − σ_★ quenching relations.