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Temperature and relative humidity (RH) are the most important thermodynamic parameters in aerosol formation, yet laboratory studies of nucleation and growth dependencies on temperature and RH are lacking. Here we report the experimentally observed temperature and RH dependences of sulfuric acid aerosol nucleation and growth. Experiments were performed in a flow tube in the temperature range from 248 to 313 K, RH from 0.8% to 79%, and relative acidity (RA) of sulfuric acid from 6 x 10(-5) to 0.38 (2 x 10(7)-10(9) cm(-3)). The impurity levels of base compounds were determined to be NH3 < 23 pptv (parts per thousand by volume), methylamine < 1.5 pptv, and dimethylamine < 0.52 pptv. Our results showed that low temperatures favor nucleation at fixed sulfuric acid concentration but impede nucleation when RA is fixed. It is also shown that binary nucleation of sulfuric acid and water is negligible in planetary boundary layer temperature and sulfuric acid ranges. An empirical algorithm was derived to correlate the nucleation rate with RA, RH, and temperature together. Collision-limited condensation of free-sulfuric acid molecules fails to predict the observed growth rate in the sub-3nm size range, as well as its dependence on temperature and RH. This suggests that evaporation, sulfuric acid hydration, and possible involvement of other ternary molecules should be considered for the sub-3nm particle growth.