Do you want to be known as X's disciple, or as the Y's teacher? Do you see yourself as a theorist, a critic, or a scholar? Are you mainly an expert on Joyce or Twain, or on Ireland or Sweden? Do you define yourself by period or by theoretical approach?
In my case, I don't want disciples, nor to be known for whom I worked with. I'd like to be thought of as someone who defined the terms of the debate in my field, someone who raised the standard for what excellent work is in my subfield, and made this subfield relevant to those for whom it would otherwise not be so important. I want to have a reputation both in Spain and in the US academy. I don't need to be a star; I'd rather be respected by a few people who know quality work.