Abstract: Process for the conversion of heavy feedstocks selected from heavy crude oils, distillation residues, heavy oils coming from catalytic treatment, thermal tars, oil sand bitumens, various kinds of coals and other high-boiling feedstocks of a hydrocarbon origin known as black oils, by the combined use of the following three process units: hydroconversion with catalysts in slurry phase (HT), distillation or flash (D), deasphalting (SDA), comprising the following steps: mixing at least part of the heavy feedstock and/or at least most of the stream containing asphaltenes obtained in the deasphalting unit with a suitable hydrogenation catalyst and sending the mixture obtained to a hydrotreatment reactor (HT) into which hydrogen or a mixture of hydrogen and H2S is charged; sending the stream containing the hydrotreatment reaction product and the catalyst in dispersed phase to one or more distillation or flash steps (D) whereby the different fractions coming from the hydrotreatment reaction are separated; recycling a