Some questions come to mind, like:
1. In what part of the new paper shall an author self-cite a previous research of his/her own? the introduction? results? discussion?
2. In what part of the new paper does self-citation increase the most its significance?
3. Shall the author's new papers be self-cited or the old ones?
4. Does self-citation in the discussion support the findings?
5. Does self-citation increase the impact of the paper? its citation? its merit? the popularity of the author?
6. Is it preferable that the papers the author has second-authored be self-cited more than the those first-authored?
7. In what cases might self-citation hurt the chances of the new paper to be published successfully?