The ab initio determination of the character and properties of electronic excited states (ES) is the cornerstone of modern theoretical photochemistry. Yet, traditional ES methods become readily impractical when applied to fairly large molecules, or when used on thousands of different systems. In contrast, Machine Learning (ML) techniques have demonstrated their accuracy at retrieving ES properties of large molecular databases at a reduced computational cost. Especially for excited states applications, non-linear algorithms tend to be specialized and to target only individual properties. Learning fundamental quantum chemical objects potentially represents a more efficient, yet complex, alternative as a large number of molecular properties could be then extracted through post-processing. Herein, we report the general framework able to learn three fundamental objects of an ES: the hole and particle densities, as well as the transition density. We demonstrate the advantages of targeting those outputs of an ES computation, and address the additional complexity of learning 3-dimensional scalar fields. We apply our predictions to obtain a list of derived properties, including the state character and the topological descriptors of the exciton, for the two bands (nπ and ππ) of a collection of 3432 azoheteroarene photoswitches. In doing so, we prove that the proposed approach offers a way to access ES information of different kinds, bypassing the need of traditional electronic structure computations, while retaining ab initio accuracy.