A catalyst for hydrotreating residual petroleum oil has a pore size distribution related to the measured size distribution of sulfur, nickel and vanadium containing molecules in the residual oil to be hydrotreated. The size distribution of the sulfur, nickel and vanadium containing molecules in the residual oil is measured by gel permeation chromatography. From this measured size distribution, the catalyst pore size distribution which produces desired demetalization and desulfurization is determined for specified process conditions. A catalyst having the determined pore size distribution is produced by calcining alumina at different temperatures to produce alumina with the determined pore size distribution. The alumina is impregnated with cobalt molybdenum to produce the catalyst which is tailored to produce the desired demetalization and desulfurization of the residual oil to be treated.