  The nature and origin of supermassive black holes (SMBHs) remain an open
matter of debate within the scientific community. While various theoretical
scenarios have been proposed, each with specific observational signatures, the
lack of sufficiently sensitive X-ray observations hinders the progress of
observational tests. In this white paper, we present how AXIS will contribute
to solving this issue. With an angular resolution of 1.5$^{\prime\prime}$
on-axis and minimal off-axis degradation, we have designed a deep survey
capable of reaching flux limits in the [0.5-2] keV range of approximately
2$\times$10$^{-18}$ \fcgs~ over an area of 0.13 deg$^2$ in approximately 7
million seconds (7 Ms). Furthermore, we have planned an intermediate depth
survey covering approximately 2 deg$^2$ and reaching flux limits of about
2$\times$10$^{-17}$ \fcgs ~ in order to detect a significant number of SMBHs
with X-ray luminosities (L$_X$) of approximately 10$^{42}$ \lx up to z$\sim$10.
These observations will enable AXIS to detect SMBHs with masses smaller than
10$^5$ \ms, assuming Eddington-limited accretion and a typical bolometric
correction for Type II AGN. AXIS will provide valuable information on the
seeding and population synthesis models of SMBH, allowing for more accurate
constraints on their initial mass function (IMF) and accretion history from
z$\sim$0-10. To accomplish this, AXIS will leverage the unique synergy of
survey telescopes such as JWST, Roman, Euclid, LSST, and the new generation of
30m class telescopes. These instruments will provide optical identification and
redshift measurements, while AXIS will discover the smoking gun of nuclear
activity, particularly in the case of highly obscured AGN or peculiar UV
spectra as predicted and recently observed in the early Universe.
