A Yid in Tiveriah related to Rav Moshe Shternbuch that after the petirah of Rav Yosef Shalom Elyashiv zt”l, he asked Rav Chaim Kanievsky who should then be turned to for psak halacha. “Rav Chaim told me that I should go to Rav Moshe Shternbuch, and what he paskens is what I should do!”