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We present EMERGE, an Empirical ModEl for the foRmation of GalaxiEs,describing the evolution of individual galaxies in large volumes from $z\sim10$to the present day. We assign a star formation rate to each dark matter halobased on its growth rate, which specifies how much baryonic material becomesavailable, and the instantaneous baryon conversion efficiency, which determineshow efficiently this material is converted to stars, thereby capturing thebaryonic physics. Satellites are quenched following the delayed-then-rapidmodel, and they are tidally disrupted once their subhalo has lost a significantfraction of its mass. The model is constrained with observed data extending outto high redshift. The empirical relations are very flexible, and the modelcomplexity is increased only if required by the data, assessed by several modelselection statistics. We find that for the same final halo mass galaxies canhave very different star formation histories. Nevertheless, the average starformation and accretion rates are in good agreement with models following anabundance matching strategy. Galaxies that are quenched at $z=0$ typically havea higher peak star formation rate compared to their star-forming counterparts.The accretion of stars can dominate the total mass of massive galaxies, but isinsignificant for low-mass systems, independent of star-formation activity.EMERGE predicts stellar-to-halo mass ratios for individual galaxies andintroduces scatter self-consistently. We find that at fixed halo mass, passivegalaxies have a higher stellar mass on average. The intra-cluster-mass inmassive haloes can be up to 8 times larger than the mass of the central galaxy.Clustering for star-forming and quenched galaxies is in good agreement withobservational constraints, indicating a realistic assignment of galaxies tohaloes.

EMERGE - An empirical model for the formation of galaxies since $z\sim10$