The present invention concerns the use of a catalyst comprising an extruded essentially alumina-based support, constituted by a plurality of juxtaposed agglomerates and partially in the form of packs of flakes and partially in the form of needles, and optionally comprising at least one catalytic metal or a compound of a catalytic metal from group VIB and/or at least one catalytic metal or compound of a catalytic metal from group VIII, further comprising at least one dopant selected from the group formed by boron, phosphorous, silicon (or a silica different from that which can be found in the support) and halogens, in an ebullating bed process and for hydrorefining and hydroconverting hydrocarbon feeds.