  The analysis of galaxies on the star formation rate - stellar mass (SFR-M*)
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* 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 $\rm
log_{10}(sSFR/yr^{-1}) > -9.8$, 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 ~5% of all galaxies at
z=0.5-1.0, while they account for ~16% of galaxies at 2$<z<$3 with
log$_{10}(M^{*})=$8.25-11.25. We conclude that the dissection of the SFR-M* 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.
