The invention relates to a process for converting heavy hydrocarbonaceous feedstocks carried out in a slurry reactor in the presence of hydrogen and in the presence of a catalytic composition obtained by: injecting a catalytic precursor of at least one metal of Group VIB and/or Group VIII in at least part of the feedstock to be treated in the absence of an oxide substrate, thermal treatment at a temperature of 400.degree. C. or below, in the presence of H.sub.2S so as to form the dispersed sulphur-containing catalyst, bringing said catalyst into contact with particles of alumina oxide free from silica, said oxide particles having a polymodal porous structure composed of a plurality of juxtaposed agglomerates and each formed from a plurality of acicular platelets, the platelets of each agglomerate being oriented radially in relation to one another and relative to the centre of the agglomerate, said particles having an irregular non-spherical shape and being mainly in the form of fragments obtained by crushing with alumina balls, introducing the catalyst composition obtained into the reactor.