There are various duties of a delegate administrator. Primarily, a delegate administrator should be capable of creating and editing users in particular and subordinate roles. They are also often required to assign users to their specific profiles. They are also required to manage and to customize various different aspects of a custom object.
However, modifying or creating relationships on an object is something that which a delegate administrator is usually not expected to do. Other duties include resetting passwords, creation of public groups and the management of members in those public groups. All the above mentioned tasks may fall under the duties of a delegate administrator.