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We study the formation of over 6000 compact groups (CGs) of galaxiesidentified in mock redshift-space galaxy catalogues built from semi-analyticalmodels of galaxy formation (SAMs) run on the Millennium Simulations. We selectCGs of 4 members in our mock SDSS galaxy catalogues and, for each CG, we traceback in time the real-space positions of the most massive progenitors of their4 galaxies. By analysing the evolution of the distance of the galaxy members tothe centre of mass of the group, we identify 4 channels of CG formation. Theclassification of these assembly channels is performed with an automatic recipeinferred from a preliminary visual inspection and based on the orbit of thegalaxy with the fewest number of orbits. Most CGs show late assembly, with thelast galaxy arriving on its first or second passage, while only 10-20 per centform by the gradual contraction of their orbits by dynamical friction, and onlya few per cent forming early with little subsequent contraction. However, a SAMfrom a higher resolution simulation leads to earlier assembly. Assemblyhistories of CGs also depend on cosmological parameters. At similar resolution,CGs assemble later in SAMs built on parent cosmological simulations of highdensity parameter. Several observed properties of mock CGs correlate with theirassembly history: early-assembling CGs are smaller, with shorter crossingtimes, and greater magnitude gaps between their brightest two members, andtheir brightest galaxies have smaller spatial offsets and are more passive.

Compact groups from semi-analytical models of galaxy formation -- II: Different assembly channels