When you delegate someone for specific task(s), the assigned person becomes responsible only for the specified task(s).
By the User
If you have something urgent and you know you can’t make time for the tasks that 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;
Recently Used
You can see last selected in there.
Organization
When clicked on the organization text box a pop up window appears and also when you click on the plus you will see department name and when you click on plus the near to department then you will see users name or users position.
Search Results
If you cannot find the user or users you need, you can type her/his 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 :