When you delegate someone for specific task(s), the assigned person becomes responsible only for the related task(s).
By the User
If you have something urgent and you know you can’t make time for the tasks that are assigned to you, open the related task window and you will see the “Forward” button in the navigation as shown below in the picture with three options:
You can see the last ones selected in there.
You can reach organization database with it.
When clicking the organization text box, a pop up window appears, and also when you click on the plus, you will see a department name. When you click on the plus near the department, you will see user's name or user's position.
If you cannot find the user or users you need, you can type their name to search for it, or you can just click on the search results button to look for it.
After this, when you click OK button, the person you selected will be assigned to the task you wanted to.
You can learn how to forward a task by watching this video :