Automation can be considered as a design alternative that brings the benefits of reducing the potential for human error and of increasing performance. However, badly designed automations, of which some of them are called automation surprises, can have a very negative impact on the overall performance of the couple operator/system. Automation design requires the definition of three specific aspects defining the relationship between the user and the system: allocation of functions, authority and responsibility. While these abstract concepts are usually well understood at a high level of abstraction, their integration within a development process is cumbersome. This paper presents an approach based on task models to explicitly handle those concepts. We show how such concepts can be integrated in a task modeling notation and illustrate on a case study how this notation can be used to describe design alternatives with different allocation of functions, authority and responsibility between the user and the system. Exploiting the case study, we demonstrate that embedding explicitly these concepts in a notation supports analysis and assessment of automation designs.