Doctoral education and supervision have changed in recent decades. The increasing prevalence of co-supervision has been a notable aspect of this, but change also includes stricter accountability and quality assurance measures, such as the quantification of workload allocations in supervision as well as of academic work more broadly. This paper focuses on challenging issues pertaining to such workload allocation in co-supervision, an important and underexplored feature of doctoral supervision, with the aim of informing policy and improving practice. This qualitative study was conducted in a research-intensive university and data sources were semi-structured interviews with 14 academic staff across multiple disciplines plus a short survey comprising mostly of open-ended questions completed by 106 participants. These data were complimented with institutional supervisor workload allocations. Ambiguity was found to be a dominant feature of the co-supervision allocations and this had both advantages and disadvantages. The concept of 'supervision peripherality' is introduced to capture the phenomenon of co-supervisors with a very low share of supervision, which we argue is a phenomenon that challenges what constitutes being a doctoral supervisor and thus warrants further exploration. We also argue institutions should examine the adequacy of having such peripheral supervisors in order to determine when these are truly required.