  Two main modes of star formation are know to control the growth of galaxies:
a relatively steady one in disk-like galaxies, defining a tight star formation
rate (SFR)-stellar mass sequence, and a starburst mode in outliers to such a
sequence which is generally interpreted as driven by merging. Such starburst
galaxies are rare but have much higher SFRs, and it is of interest to establish
the relative importance of these two modes. PACS/Herschel observations over the
whole COSMOS and GOODS-South fields, in conjunction with previous
optical/near-IR data, have allowed us to accurately quantify for the first time
the relative contribution of the two modes to the global SFR density in the
redshift interval 1.5<z<2.5, i.e., at the cosmic peak of the star formation
activity. The logarithmic distributions of galaxy SFRs at fixed stellar mass
are well described by Gaussians, with starburst galaxies representing only a
relatively minor deviation that becomes apparent for SFRs more than 4 times
higher than on the main sequence. Such starburst galaxies represent only 2% of
mass-selected star forming galaxies and account for only 10% of the cosmic SFR
density at z~2. Only when limited to SFR>1000M(sun)/yr, off-sequence sources
significantly contribute to the SFR density (46+/-20%). We conclude that
merger-driven starbursts play a relatively minor role for the formation of
stars in galaxies, whereas they may represent a critical phase towards the
quenching of star formation and morphological transformation in galaxies.
