  The many unique properties of galaxies are shaped by physical processes that
affect different components of the galaxy - like the bulges and discs - in
different ways, and leave characteristic imprints on the light and spectra of
these components. Disentangling their spectra can reveal vital clues that can
be traced back in time to understand how galaxies, and their components, form
and evolve throughout their lifetimes. With BUDDI, we have decomposed the IFU
datacubes in SDSS-MaNGA DR17 into a S\'ersic bulge component and an exponential
disc component and extracted their clean bulge and disc spectra. BUDDI-MaNGA is
the first and largest statistical sample of such decomposed spectra of 1452
galaxies covering morphologies from ellipticals to late-type spirals. We
derived stellar masses of the individual components with SED fitting using
BAGPIPES and estimated their mean mass-weighted stellar metallicities and
stellar ages using pPXF. With this information in place, we reconstructed the
mass assembly histories of the bulges and discs of the 968 spiral galaxies
(Sa-Sm Types) in this sample to look for systematic trends with respect to
stellar mass and morphology. Our results show a clear downsizing effect
especially in the bulges, with more massive components assembling earlier and
faster than the less massive ones. Additionally, on comparing the stellar
populations of the bulges and discs in these galaxies, we find that a majority
of the bulges host more metal-rich and older stars than their disc
counterparts. Nevertheless, we also find that there exists a non-negligible
fraction of the spiral galaxy population in our sample with bulges that are
younger and more metal-rich than their discs. We interpret these results,
taking into account how their formation histories and current stellar
populations depend on stellar mass and morphology.
