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Generative models are undoubtedly a hot topic in Artificial Intelligence, among which the most common type is Generative Adversarial Networks (GANs). These architectures let one synthesise artificial datasets by implicitly modelling the underlying probability distribution of a real-world training dataset. With the introduction of Conditional GANs and their variants, these methods were extended to generating samples conditioned on ancillary information available for each sample within the dataset. From a practical standpoint, however, one might desire to generate data conditioned on partial information. That is, only a subset of the ancillary conditioning variables might be of interest when synthesising data. In this work, we argue that standard Conditional GANs are not suitable for such a task and propose a new Adversarial Network architecture and training strategy to deal with the ensuing problems. Experiments illustrating the value of the proposed approach in digit and face image synthesis under partial conditioning information are presented, showing that the proposed method can effectively outperform the standard approach under these circumstances.