Integrating information while recognizing dependence from multiple data sources and enhancing the predictive performance of the multi-output regression are challenging tasks. Multioutput Gaussian Process (MOGP) methods offer outstanding solutions with tractable predictions and uncertainty quantification. However, their practical applications are hindered by high computational complexity and storage demand. Additionally, there exist model mismatches in existing MOGP models when dealing with non-Gaussian data. To improve the model representation ability in terms of flexibility, optimality, and scalability, this paper introduces a novel multi-output regression framework, termed Graphical MOGP (GMOGP), which is empowered by: (i) Generating flexible Gaussian process priors consolidated from dentified parents, (ii) providing dependent processes with attention-based graphical representations, and (iii) achieving Pareto optimal solutions of kernel hyperparameters via a distributed learning framework. Numerical results confirm that the proposed GMOGP significantly outperforms state-of-the-art MOGP alternatives in predictive performance, as well as in time and memory efficiency, across various synthetic and real datasets.