This article conducts a large dimensional study of a simple yet quite versatile classification model, encompassing at once multi-task and semi-supervised learning, and taking into account uncertain labeling. Using tools from random matrix theory, we characterize the asymptotics of some key functionals, which allows us on the one hand to predict the performances of the algorithm, and on the other hand to reveal some counter-intuitive guidance on how to use it efficiently. The model, powerful enough to provide good performance guarantees, is also straightforward enough to provide strong insights into its behavior.