  We present a structural and morphological catalogue for 45 million objects
selected from the first year of data from the Dark Energy Survey (DES). Single
Sersic fits and non-parametric measurements are produced for g, r and i
filters. The parameters from the best-fitting Sersic model (total magnitude,
half-light radius, Sersic index, axis ratio and position angle) are measured
with Galfit; the non-parametric coefficients (concentration, asymmetry,
clumpiness, Gini, M20) are provided using the Zurich Estimator of Structural
Types (ZEST+). To study the statistical uncertainties, we consider a sample of
state-of-the-art image simulations with a realistic distribution in the input
parameter space and then process and analyse them as we do with real data: this
enables us to quantify the observational biases due to PSF blurring and
magnitude effects and correct the measurements as a function of magnitude,
galaxy size, Sersic index (concentration for the analysis of the non-parametric
measurements) and ellipticity. We present the largest structural catalogue to
date: we find that accurate and complete measurements for all the structural
parameters are typically obtained for galaxies with SExtractor MAG AUTO I < 21.
Indeed, the parameters in the filters i and r can be overall well recovered up
to MAG AUTO < 21.5, corresponding to a fitting completeness of ~90% below this
threshold, for a total of 25 million galaxies. The combination of parametric
and non-parametric structural measurements makes this catalogue an important
instrument to explore and understand how galaxies form and evolve. The
catalogue described in this paper will be publicly released alongside the Dark
Energy Survey collaboration Y1 cosmology data products at the following URL:
https://des.ncsa.illinois.edu/releases/y1a1/gold/morphology.
