We propose the first large-scale message passing distributed scheme for parallelizing the computational flow of Moea/d, a popular decomposition-based evolutionary multiobjective optimization algorithm. We show how synchronicity and workload granularity can impact both quality and computing time, in an extremely fine-grained configuration where each individual in the Moea/d population is mapped to a single distributed processing unit. More specifically, we deploy our distributed protocol using a large-scale environment of 128 computing cores and conduct a throughout analysis using a broad range of bi-objective combinatorial ρMNK-landscapes. Besides being able to show significant speed-ups while maintaining competitive search quality, our experimental results provide insights into the behavior of the proposed scheme in terms of quality/speedup trade-offs; thus pushing a step towards the achievement of effective and efficient parallel decomposition-based approaches for large-scale multi-objective optimization.