The analysis of galaxies on the star formation rate - stellar mass ( SFR- M ^ { \ast } ) plane is a powerful diagnostic for galaxy evolution at different cosmic times . We consider a sample of 24463 galaxies from the CANDELS/GOODS-S survey to conduct a detailed analysis of the SFR- M ^ { \ast } relation at redshifts 0.5 \leqslant z < 3 over more than three dex in stellar mass . To obtain SFR estimates , we utilise mid- and far-IR photometry when available , and rest-UV fluxes for all the other galaxies . We perform our analysis in different redshift bins , with two different methods : 1 ) a linear regression fitting of all star-forming galaxies , defined as those with specific star formation rates log _ { 10 } ( sSFR / yr ^ { -1 } ) > -9.8 , similarly to what is typically done in the literature ; 2 ) a multi-Gaussian decomposition to identify the galaxy main sequence ( MS ) , the starburst sequence and the quenched galaxy cloud . We find that the MS slope becomes flatter when higher stellar mass cuts are adopted , and that the apparent slope change observed at high masses depends on the SFR estimation method . In addition , the multi-Gaussian decomposition reveals the presence of a starburst population which increases towards low stellar masses and high redshifts . We find that starbursts make up \sim 5 \% of all galaxies at z = 0.5 - 1.0 , while they account for \sim 16 \% of galaxies at 2 < z < 3 with log _ { 10 } ( M ^ { * } / M _ { o } ) = 8.25-11.25 . We conclude that the dissection of the SFR- M ^ { \ast } in multiple components over a wide range of stellar masses is necessary to understand the importance of the different modes of star formation through cosmic time .