  We investigate the potential sources of theoretical systematics in the
anisotropic Baryon Acoustic Oscillation (BAO) distance scale measurements from
the clustering of galaxies in configuration space using the final Data Release
(DR12) of the Baryon Oscillation Spectroscopic Survey (BOSS). We perform a
detailed study of the impact on BAO measurements from choices in the
methodology such as fiducial cosmology, clustering estimators, random
catalogues, fitting templates, and covariance matrices.
  The theoretical systematic uncertainties in BAO parameters are found to be
0.002 in the isotropic dilation $\alpha$ and 0.003 in the quadrupolar dilation
$\epsilon$. The leading source of systematic uncertainty is related to the
reconstruction techniques. Theoretical uncertainties are sub-dominant compared
with the statistical uncertainties for BOSS survey, accounting
$0.2\sigma_{stat}$ for $\alpha$ and $0.25\sigma_{stat}$ for $\epsilon$
  ($\sigma_{\alpha,stat} \sim$0.010 and $\sigma_{\epsilon,stat}\sim$ 0.012
respectively). We also present BAO-only distance scale constraints from the
anisotropic analysis of the correlation function. Our constraints on the
angular diameter distance $D_A(z)$ and the Hubble parameter $H(z)$, including
both statistical and theoretical systematic uncertainties, are 1.5\% and 2.8\%
at $z_{\rm eff}=0.38$, 1.4\% and 2.4\% at $z_{\rm eff}=0.51$, and 1.7\% and
2.6\% at $z_{\rm eff}=0.61$. This paper is part of a set that analyzes the
final galaxy clustering dataset from BOSS. The measurements and likelihoods
presented here are cross-checked with other BAO analysis in \citet{Acacia16}.
The systematic error budget concerning the methodology on post-reconstruction
BAO analysis presented here is used in \citet{Acacia16} to produce the final
cosmological constraints from BOSS.
