The paper investigates the formation and evolution of brightest cluster galaxies (BCGs) using semi-analytic techniques and N-body simulations. It shows that BCGs form hierarchically, with their stars forming early (50% at z ~ 5, 80% at z ~ 3) in small galaxies, fueled by rapid cooling rather than mergers. Despite late mergers, BCGs appear old due to the accumulation of old stellar populations from dark matter halo mergers. The study finds that BCGs assemble late, with half their mass locked in a single galaxy by z ~ 0.5. The paper also discusses the evolution of BCGs to high redshifts, showing agreement with observations. It highlights the hierarchical link between high-z BCGs and their local counterparts, noting that high-z BCGs are part of the massive end of local BCG progenitors but are not the same galaxies. The study uses the Millennium Simulation to analyze BCG formation and evolution, finding that BCGs have a small dispersion in luminosity and stellar population at low redshift, suggesting similar formation histories. The results show that BCGs form through accretion of satellites, with a significant fraction of stars formed at high redshift. The paper concludes that the hierarchical formation model accurately describes BCG evolution, with a median mass growth factor of ~3 from z ~ 1 to z = 0, which appears to conflict with some observational data but is likely an apparent contradiction.The paper investigates the formation and evolution of brightest cluster galaxies (BCGs) using semi-analytic techniques and N-body simulations. It shows that BCGs form hierarchically, with their stars forming early (50% at z ~ 5, 80% at z ~ 3) in small galaxies, fueled by rapid cooling rather than mergers. Despite late mergers, BCGs appear old due to the accumulation of old stellar populations from dark matter halo mergers. The study finds that BCGs assemble late, with half their mass locked in a single galaxy by z ~ 0.5. The paper also discusses the evolution of BCGs to high redshifts, showing agreement with observations. It highlights the hierarchical link between high-z BCGs and their local counterparts, noting that high-z BCGs are part of the massive end of local BCG progenitors but are not the same galaxies. The study uses the Millennium Simulation to analyze BCG formation and evolution, finding that BCGs have a small dispersion in luminosity and stellar population at low redshift, suggesting similar formation histories. The results show that BCGs form through accretion of satellites, with a significant fraction of stars formed at high redshift. The paper concludes that the hierarchical formation model accurately describes BCG evolution, with a median mass growth factor of ~3 from z ~ 1 to z = 0, which appears to conflict with some observational data but is likely an apparent contradiction.