Galaxy And Mass Assembly (GAMA): $\mathcal{M_\star}-R_{\rm e}$ relations
  of $z=0$ bulges, discs and spheroids
  We perform automated bulge + disc decomposition on a sample of $\sim$7500
galaxies from the Galaxy And Mass Assembly (GAMA) survey in the redshift range
of 0.002$<$z$<$0.06 using SIGMA, a wrapper around GALFIT3. To achieve robust
profile measurements we use a novel approach of repeatedly fitting the
galaxies, varying the input parameters to sample a large fraction of the input
parameter space. Using this method we reduce the catastrophic failure rate
significantly and verify the confidence in the fit independently of $\chi^2$.
Additionally, using the median of the final fitting values and the 16$^{th}$
and 84$^{th}$ percentile produces more realistic error estimates than those
provided by GALFIT, which are known to be underestimated. We use the results of
our decompositions to analyse the stellar mass - half-light radius relations of
bulges, discs and spheroids. We further investigate the association of
components with a parent disc or elliptical relation to provide definite $z=0$
disc and spheroid $\mathcal{M_\star}-R_{\rm e}$ relations. We conclude by
comparing our local disc and spheroid $\mathcal{M_\star}-R_{\rm e}$ to
simulated data from EAGLE and high redshift data from CANDELS-UDS. We show the
potential of using the mass-size relation to study galaxy evolution in both
cases but caution that for a fair comparison all data sets need to be processed
and analysed in the same manner.
