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The evolution of dust abundance relative to the total gas content calculated by the theoretical models developed by Kuo & Hirashita (2012, MNRAS, 432, 637). The horizontal axis shows the time sequence (precisely, the oxygen abundance 12+log(O/H)). The vertical axis show the dust abundance (dust-to-gas ratio). We examine two cases: without and with small (< 0.1 μm) dust grains. Without small grains (i.e., only with large grains), the rapid increase of dust abundance due to dust growth comes later, failing to explain the observationally acceptable range (blue box) for the distant quasars. With small grains, the rapid increase of the dust abundance by dust growth occurs earlier, and the line successfully pass through the observational range (blue box), which means that we can successfully explain the dust abundance observed in the quasars. The purple and blue curves show the model with and without small grains, respectively.