We proposed a tuning-free procedure to estimate the covariate-adjusted Gaussian graphical model. For each finite subgraph, this estimator is asymptotically normal and efficient. As a consequence, a confidence interval can be obtained for each edge. We further apply the asymptotic normality result to perform support recovery through edge-wise adaptive thresholding. This support recovery procedure is called ANTAC, standing for Asymptotically Normal estimation with Thresholding after Adjusting Covariates. ANTAC is implemented as an R package.