We study low-metallicity star formation with a set of high-resolution hydrodynamics simulations for various gas metallicities over a wide range $0$--$10^{-3} {rm Z}_{bigodot}$. Our simulations follow non-equilibrium chemistry and radiative cooling by adopting realistic elemental abundances and dust size distribution. We examine the condition for the fragmentation of collapsing clouds (cloud fragmentation; CF) and of accretion discs (disc fragmentation; DF). We find that CF is suppressed due to rapid gas heating accompanied with molecular hydrogen formation, whereas DF occurs in almost all our simulations regardless of gas metallicities. We also find that, in the accretion discs, the growth of the protostellar systems is overall oligarchic. The primary protostar grows through the accretion of gas, and secondary protostars form through the interaction of spiral arms or the break-up of a rapidly rotating protostar. Despite vigorous fragmentation, a large fraction of secondary protostars are destroyed through mergers or tidal disruption events with other protostars. For a few hundred years after the first adiabatic core formation, only several protostars survive in a disc, and the total mass of protostars is $0.52$--$3.8 {rm M}_{bigodot}$.
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