This article presents the results of a cross-institutional survey on PhD students' supervision at Russian universities. It is aimed at answering three questions concerning (1) styles of PhD supervision and their prevalence, (2) the relation between supervision style and PhD students' satisfaction with their supervisor, and (3) the relation between supervision style and PhD students' expected time-to-degree. We propose the empirically driven categorization of six supervision styles: superhero, hands-off supervisor, research practice mediator, dialogue partner, mentor, and research advisor. The most problematic category, characterized by providing no help for PhD students, was named "hands-off supervisors." For this category PhD students reported the lowest level of satisfaction, and the highest expected time-to degree. Nonetheless, the large share of PhD students who are satisfied with hands-off supervisors may evidence a presence of a disengagement compact between PhD students and supervisors in Russian universities. Two categories of supervisors characterized by the highest level of PhD students' satisfaction and shortest expected time-to-degree were named "superheroes" and "mentors." These supervisors are reported to perform managerial and expert functions, which emphasizes the critical importance of these functions.