NOVELTY - The process involves fractionating a first effluent from an ebullated bed hydroconversion reactor (20) to recover a liquid product and vapor product. The vapor product and a heavy distillate feed-stock (52) are in contact with a zeolitic selective hydrocracking catalyst in an ebullated bed hydrocracking reactor system (40) to produce a second effluent. The second effluent is recovered from the ebullated bed hydrocracking reactor system. The second effluent is fractionated from the ebullated bed hydrocracking reactor system to recover hydrocarbon fractions e.g. heavy gas oil fraction (160).    USE - Process for upgrading residuum hydrocarbons e.g. petroleum crudes, shale oils, tar sands bitumen, coal-derived oils, tall oils, black oils, organic wastes, biomass-derived liquids and heavy oil residuum stream, and heavy distillate feedstocks e.g. atmospheric gas oil, light vacuum gas oil, heavy vacuum gas oil, heavy coker gas oil, FCC cycle oil and deasphalted oil derivable from petroleum, bitumen, kerogen, biomass or organic waste sources (all claimed), in petroleum refining and petrochemicals industries.    ADVANTAGE - The process enables maintaining target conversions below a level in which sediment formation becomes excessive so as to prevent continuity of operations. The process enables reducing hydrogen consumption and allowing addition of makeup catalyst without having to shutdown plant, thus leading to longer cycle times.    DETAILED DESCRIPTION - The process enables a zeolitic selective hydroconversion catalyst is selected from a group consisting of a H Y-zeolite, H ZSM-5, mordenite, erionite or ultrastable faujasite, USY zeolite, Beta zeolite, ZSM-11, ZSM-22, ZSM-23, ZSM-35, ZSM-48, ZSM-57, ZSM-34, REY molecular sieve and REHY molecular sieve. An INDEPENDENT CLAIM is also included for a system for upgrading residuum hydrocarbons and heavy distillate feedstocks.    DESCRIPTION OF DRAWING(S) - The drawing shows a flow diagram illustrating a process for upgrading residuum and heavy distillate hydrocarbon feedstocks.    Ebullated bed hydroconversion reactor (20)    Ebullated bed hydrocracking reactor system (40)    Heavy distillate feed-stock (52)    Light vacuum gas oil fraction (158)    Heavy gas oil fraction (160)