Strict antitrust sense don't look at actual monopoly to trigger, but just if you use your standing in the market to gain unjust advantages. Which does not require a monopoly situation but just a strong standing used wrong (like abusing vertical integration). So Standard Oil, to take a famous example, never had more than a 30% market share.

Breaking a monopoly can be a solution to that, however. But having a large part of a market by itself doesn't trigger anti trust legislation.