When assigning responsibilities to your supervisors or subordinates, you want to make sure of a few things. The first is to make sure that you distribute work and responsibilities as equally as possible. You don't want to overwork or under work your people. The second stablish ways of monitoring and tracking your subordinates accomplishments and tasks and workflows. You want to make sure that you foster the feeling of a hands on organized and involved manager, as opposed to a disorganized or frantic one or a micromanaging boss. The third is to establish performance metrics for them or targets they need to meet.
For example, certain number of reports generated each month, a specific number of audits and checks conducted and others. Remember, if you're in charge of a supervisor, you're assessing his or her ability to get his subordinates not himself to accomplish routine tasks.