  We study, by means of dedicated simulations of massive black hole build-up,
the possibility to constraint the existence and nature of the AGN population at
z>6 with available and planned X-ray and near infrared space telescopes. We
find that X-ray deep-field observations can set important constraints to the
faint-end of the AGN luminosity function at very high redshift. Planned X-ray
telescopes should be able to detect AGN hosting black holes with masses down to
>10^5 Msun (i.e., X-ray luminosities in excess of 10^42 erg s^-1), and can
constrain the evolution of the population of massive black hole at early times
(6<z<10). We find that this population of AGN should contribute substantially
(~25%) to the unresolved fraction of the cosmic X-ray background in the 0.5-10
keV range, and that a significant fraction (~3-4%) of the total background
intensity would remain unaccounted even after future X-ray observations. As
byproduct, we compute the expected UV background from AGN at z>6 and we discuss
the possible role of AGN in the reionization of the Universe at these early
epochs, showing that AGN alone can provide enough ionizing photons only in the
(improbable) case of an almost completely homogeneous inter-galactic medium.
Finally, we show that super-Eddington accretion, suggested by the observed QSOs
at z>6, must be a very rare event, confined to black holes living in the
highest density peaks.
