The invention involves the liquid phase hydroconversion of hydrocarbon charges containing heavy fractions, and more particularly their deep conversion, in which the charge is contacted with a dispersed catalyst in the presence of a polyaromatic additive. The catalyst is a sulfide of a hydrogenating metal (such as molybdenum, nickel or cobalt) generated in situ from a precursor. The additive has at least three aromatic cycles, has a boiling point exceeding 300.degree. C., and is added at a rate of 5 to 60% by weight based on the charge. Synergism between the catalyst and the additive makes it possible to reduce the catalyst quantity and/or improve the conversion and quality of the products.