  We examine a sample of 1495 galaxies in the CANDELS fields to determine the
evolution of two component galaxies, including bulges and discs, within massive
galaxies at the epoch 1 < z < 3 when the Hubble sequence forms. We fit all of
our galaxies' light profiles with a single S\'ersic fit, as well as with a
combination of exponential and S\'ersic profiles. The latter is done in order
to describe a galaxy with an inner and an outer component, or bulge and disc
component. We develop and use three classification methods (visual, F-test and
the RFF) to separate our sample into 1-component galaxies (disc/spheroids-like
galaxies) and 2-component galaxies (galaxies formed by an 'inner part' or bulge
and an 'outer part' or disc). We then compare the results from using these
three different ways to classify our galaxies. We find that the fraction of
galaxies selected as 2-component galaxies increases on average 50 per cent from
the lowest mass bin to the most massive galaxies, and decreases with redshift
by a factor of four from z = 1 to z = 3. We find that single S\'ersic
'disc-like' galaxies have the highest relative number densities at all
redshifts, and that 2-component galaxies have the greatest increase and become
at par with S\'ersic discs by z = 1. We also find that the systems we classify
as 2-component galaxies have an increase in the sizes of their outer
components, or 'discs', by about a factor of three from z = 3 to z = 1.5, while
the inner components or 'bulges' stay roughly the same size. This suggests that
these systems are growing from the inside out, whilst the bulges or protobulges
are in place early in the history of these galaxies. This is also seen to a
lesser degree in the growth of single 'disc-like' galaxies vs. 'spheroid-like'
galaxies over the same epoch.
