  The phase diagram of the high-Tc cuprates is dominated by the Mott insulating
phase of the parent compounds. As we approach it from large doping, a standard
Fermi-liquid gradually turns into a bad non-Fermi liquid metal, a process which
culminates in the pseudogap regime, in which the antinodal region in momentum
space acquires a gap before reaching a fully gapped Mott state.
  Here we show that experiments for electron- and hole-doped BaFe2As2 support
an analogous scenario. The doping evolution is dominated by the influence of a
Mott insulator that would be realized for half-filled conduction bands, while
the stoichiometric compound does not play a special role. Weakly and strongly
correlated conduction electrons coexist in much of the phase diagram, a
differentiation which increases with hole doping. We identify the reason for
this selective Mottness in a strong Hund's coupling, which decouples the
different orbitals. Each orbital then behaves as a single band Hubbard model,
where the correlation degree only depends on how doped is each orbital from
half-filling. Our scenario reconciles contrasting evidences on the electronic
correlation strength and establishes a deep connection with the cuprates.
