The 1908 presidential election saw William Howard Taft, with the support of Theodore Roosevelt, run against William Jennings Bryan. It had been assumed that Taft himself would continue many of Roosevelt's policies, and Roosevelt himself campaigned extensively for him. However, after Taft's election, his relationship with Roosevelt would sour. Thus, in the 1912 election, with Taft running for a second term, Theodore Roosevelt would enter the race, splitting the Republican vote and leading to Woodrow Wilson's victory. With all this in mind, one might get the sense that Taft's own presidency very much unfolded under his predecessor's shadow, and he was never able to fully escape it (at least, not in his tenure as President).
This points to one of the most significant legacies of Roosevelt's presidency, and one of the factors that makes him such a towering figure in US political history. Roosevelt was charismatic and energetic in a way few presidents before him had ever been, and in this respect, he also significantly increased the power of the executive branch. Consider, for example, that he was the first president to actively prosecute big business interests (for which he received his reputation as a "Trust Buster"), was critical in shaping the passage of the Pure Food and Drug Act, and initiated efforts towards environmental conservation. In these respects, his actions as president reflected his public persona as a man of action, and Roosevelt's example has largely shaped the modern vision of the president as the dominant figure in American politics.