  We investigate, for the first time at z~3, the clustering properties of 189
Type 1 and 157 Type 2 X-ray active galactic nuclei (AGN) of moderate luminosity
(log<Lbol> = 45.3 erg/s), with photometric or spectroscopic redshifts in the
range 2.2<z<6.8. These samples are based on Chandra and XMM-Newton data in
COSMOS. We find that Type 1 and Type 2 COSMOS AGN at z=3 inhabit DMHs with
typical mass of logMh = 12.84+0.10/-0.11 and 11.73+0.39/-0.45 Msun/h,
respectively. This result requires a drop in the halo masses of Type 1 and 2
COSMOS AGN at z~3 compared to z<2 XMM COSMOS AGN with similar luminosities.
Additionally, we infer that unobscured COSMOS AGN at z~3 reside in 10 times
more massive halos compared to obscured COSMOS AGN, at 2.6sigma level. This
result extends to z~3 that found in COSMOS at z<2, and rules out the picture in
which obscuration is purely an orientation effect. A model which assumes that
the AGN activity is triggered by major mergers is quite successful in
predicting both the low halo mass of COSMOS AGN and the typical mass of
luminous SDSS quasars at z~3, with the latter inhabiting more massive halos
respect to moderate luminosity AGN. Alternatively we can argue, at least for
Type 1 COSMOS AGN, that they are possibly representative of an early phase of
fast (i.e. Eddington limited) BH growth induced by cosmic cold flows or disk
instabilities. Given the moderate luminosity, these new fast growing BHs have
masses of e7-8 Msun at z~3 which might evolve into e8.5-9 Msun mass BHs at z=0.
Following our clustering measurements, we argue that this fast BH growth at z~3
in AGN with moderate luminosity occurs in DMHs with typical mass of 6 times e12
Msun/h.
