Many have argued that Rav Chaim shlita was the top gadol hador since Rav Elyashiv was niftar, like GAON said above, and Rav Shteinman zt’l and Rav Auerbach shlita came just after Rav Chaim.
A big reason why Rav Shteinman was accepted as the successor to Rav Elyashiv is because Rav Chaim told Klal Yisroel to do so.