In the quest for more efficient air traffic management, a common approach is to allocate an increasing amount of functionality to higher levels of automation, with a supervisory role for humans. This potentially leads to forthcoming issues such as skill degradation and out-of-the-loop phenomenon. If the traffic in an airspace is instead shared between a human operator and an automated system, with specific flights fully delegated to automation, operators can maintain their skills and stay actively involved in controlling the rest of the traffic. This does, however, lead to new forms of mixed conflicts, where two flights are controlled by different agents. A smart flight allocation strategy, starting with the delegation of basic flights requiring little monitoring or cognitive effort, is expected to improve combined human-automation performance. In this paper, we present flowcharts to model en-route air traffic controller cognitive think and action processes in two core tasks: conflict detection and resolution. We qualitatively describe the impact of delegating flights to automation and the associated introduction of mixed conflicts. Once empirically validated and quantified in follow-up research, these models can be used to design flight allocation strategies for future human-automation teams.