  Context. Observations indicate a strong link between star formation and black
hole (BH) growth, but some questions remain unanswered: whether both activities
are coeval or whether one precedes the other, what their characteristic
timescales are, and what kinds of physical processes are responsible for this
interplay.
  Aims. We examine stellar and BH masses (M_star and M_BH) in z~2 active
systems at the peak of their AGN or star formation activity to investigate how
they are linked and whether AGN radiative or else radio power provides a
feedback mechanism that regulates the stellar growth in these systems.
  Methods. We analyze the infrared (IR) spectral energy distributions of radio,
sub-millimeter and mid-IR selected AGNs at z~1-3 and constrain their stellar
and AGN luminosities using AGN and host-galaxy templates.
  Results. We find evidence of increasing stellar light, thereby decreasing the
AGN mid-IR power going from mid-IR selected AGNs, to radio galaxies, and to
sub-millimeter AGNs. This trend can be explained by either decreasing Eddington
ratios or increasing offsets from the local M_BH-M_star relation. All systems
are characterized by high star formation rates regardless of their different
AGN powers, thus neither AGN radiative power nor AGN-driven radio activity
seems to influence the star formation rate in the selected AGNs. We discuss two
possible evolutionary scenarios that might link these three AGN classes.
