  The presence of supermassive black holes at redshift z > 6 raises some
questions about their formation and growth in the early universe. Due to the
construction of new telescopes like the ELT to observe and detect SMBHs, it
will be useful to derive theoretical estimates for the population and to
compare observations and model predictions in the future. In consequence our
main goal is to estimate the population of SMBHs using a semi-analytic code
known as Galacticus which is a code for the formation and evolution of galaxies
where we are about to include different scenarios for SMBHs formation
indicating the initial mass of the black hole seed, its formation conditions
and recipes for the evolution of the components of the galaxies. We found that
the principal mechanism of growing SMBHs is is via galaxy mergers and accretion
of matter. For the comparison of our results with observations, we calculate
the radius of influence of the black hole to estimate which part of the
population could be detected, leading to relations similar to the observed
ones.
