Drug design is both a time consuming and expensive endeavour. Computational strategies offer viable options to address this task; deep learning approaches in particular are indeed gaining traction for their capability of dealing with chemical structures. A straightforward way to represent such structures is via their molecular graph, which in turn can be naturally processed by graph neural networks. This paper introduces AMCG, a dual atomic-molecular, conditional, latent-space, generative model built around graph processing layers able to support both unconditional and conditional molecular graph generation. Among other features, AMCG is a one-shot model allowing for fast sampling, explicit atomic type histogram assignation and property optimization via gradient ascent. The model was trained on the Quantum Machines 9 (QM9) and ZINC datasets, achieving state-of-the-art performances. Together with classic benchmarks, AMCG was also tested by generating large-scale sampled sets, showing robustness in terms of sustainable throughput of valid, novel and unique molecules.