Within a cosmological hydrodynamical simulation , we form a disc galaxy with sub-components which can be assigned to a thin stellar disc , thick disk , and a low mass stellar halo via a chemical decomposition . The thin and thick disc populations so selected are distinct in their ages , kinematics , and metallicities . Thin disc stars are young ( < 6.6Â Gyr ) , possess low velocity dispersion ( \sigma _ { U,V,W } = 41 , 31 , 25 Â km s ^ { -1 } ) , high [ Fe/H ] , and low [ O/Fe ] . Conversely , the thick disc stars are old ( 6.6 < age < 9.8Â Gyrs ) , lag the thin disc by \sim 21Â km/s , possess higher velocity dispersion ( \sigma _ { U,V,W } = 49 , 44 , 35 Â km s ^ { -1 } ) , and have relatively low [ Fe/H ] and high [ O/Fe ] . The halo component comprises less than 4 % of stars in the “ solar annulus ” of the simulation , has low metallicity , a velocity ellipsoid defined by ( \sigma _ { U,V,W } = 62 , 46 , 45 Â km s ^ { -1 } ) and is formed primarily in-situ during an early merger epoch . Gas-rich mergers during this epoch play a major role in fuelling the formation of the old disc stars ( the thick disc ) . We demonstrate that this is consistent with studies which show that cold accretion is the main source of a disc galaxy ’ s baryons . Our simulation initially forms a relatively short ( scalelength \sim 1.7 kpc at z =1 ) and kinematically hot disc , primarily from gas accreted during the galaxy ’ s merger epoch . Far from being a competing formation scenario , we show that migration is crucial for reconciling the short , hot , discs which form at high redshift in \Lambda CDM , with the properties of the thick disc at z =0 . The thick disc , as defined by its abundances maintains its relatively short scale-length at z = 0 ( 2.31 kpc ) compared with the total disc scale-length of 2.73 kpc . The inside-out nature of disc growth is imprinted the evolution of abundances such that the metal poor \alpha -young population has a larger scale-length ( 4.07 kpc ) than the more chemically evolved metal rich \alpha -young population ( 2.74 kpc ) .