  Radio emission is insensitive to dust obscuration, and the breadth of the
radio luminosity function ensures that sources are detected over a wide range
of redshifts at all radio flux densities. As a result, radio continuum
observations are an efficient and unbiased probe of both nuclear (AGN) and
star-forming activity over all cosmic epochs.
  The SKA's ``ultra-deep radio continuum surveys'' will provide the answers to
at least three key astrophysical questions: (i) the star-formation history of
the Universe, (ii) the evolution of the low-power end of the radio galaxy
luminosity function and (iii) the relationship between the radio-loud AGN,
star-formation and radio-quiet AGN phenomena.
  In this paper we discuss the AGN science that will be enabled by the deep
radio continuum studies using the SKA. It is important to recognise that the
sub-microJy SKA sky will be dominated by populations other than `radio-loud'
AGN. In this way the SKA will not only provide an unbiased tracer of the
star-formation history of the Universe but also be able to study the
populations of sources we currently describe as `radio-quiet'. To illustrate
this point we present simulations of the extragalactic radio sky based from
models of the evolution of the radio luminosity function. From these
simulations we predict typical source distributions and estimate the natural
confusion limit to ultra-faint flux density limits relevant to the science and
design goals of the SKA.
