Résumé
The Type-II Seesaw Model provides an attractive scenario to account for Majorana-neutrino masses. Its extended Higgs sector, if sufficiently light, can have a rich and distinctive phenomenology at the LHC while yielding automatically an essentially Standard-Model-Higgs-like state. Several phenomenological studies have been devoted to the scalar sector of this model, as well as experimental searches focusing mostly on the (doubly-)charged states. In this paper we present an exhaustive study of the main production and decay channels of all the non-standard scalar states originating from the $SU(2)_L$ doublet and a complex triplet of the model. We stick to scenarios where lepton-number-violating decays are suppressed, for which present experimental limits are still weak, highlighting theoretical parameter sensitivities that were not previously emphasized in the literature and the uncertainties they can induce for the experimental searches at the LHC. A comprehensive classification of the various cascade decays and corresponding Standard Model particle multiplicities is provided. As an illustration, a detailed prospective search study at the LHC with an ATLAS-like detector is carried out on some benchmark points, for charged, doubly-charged, and, for the first time, neutral state productions