I have a customer who wanted to be able to assign project plan tasks to a team resource, then have the actual users self assign those tasks from My Tasks in PWA.  What she was asking for is called team assignment pooling.

You can use teams to pool assignments under a single resource where they can be later reassigned to other resources. For example, you could create a team resource named "Development" to which you assign software development tasks. By assigning this resource to the Development team and selecting the Team Assignment Pool check box, you enable other users on the Development team to see any tasks assigned to the Development resource and to accept the assignments in PWA. You could also select Team Assignment Pool for a team lead and have all assignments go through that person for distribution to team members.

Here's how you go about setting this up...

Setup the lookup table and custom field.
1. As an administrator, go to PWA > Server Settings > Enterprise Custom Fields. 
2. Create a custom lookup table called Team Name and populate it with the team names that you want to use.  In this example, I used “Team 1 DEV”.  You might use DEV Team 1, DEV Team 2, etc.  Try to avoid using managers' names in the team names because they will change every so often.
3. Edit the Team Name custom field to use the new Team Name lookup table.  You will be asked if you want to make the association permanent; you do.

Configure users.
4. As an administrator, go to PWA > Server Settings > Manager Users.
5. Edit user account.
6. In Team Details section, check the Team Assignment Pool box and select "Team 1 DEV". 
7. Repeat for any other users on Team 1 DEV.  Additionally, you can make these edits from Resource Center by multi-selecting and choosing to Edit Resource or clicking Open in the Editing group of the Resources ribbon.

Create team assignment pool resource.
8. While in Manage Users, create a Work resource called "Team 1 DEV Resource" and set its Team Details field to Team 1 DEV in the same manner.

Create project plan
9. Create project plan in Project Pro.
10. Build Team from Enterprise and add Team 1 DEV and the resource who are part of Team 1 DEV.
11. Assign appropriate tasks to Team 1 DEV Resource user.
12. Save and publish.

User Actions
13. Log into PWA as a regular user.
14. Go to Tasks.
15. From the Tasks ribbon, click Insert Team Tasks.
16. Select the checkbox for the task you will assign yourself to.
17. Click Assign to Me from the Tasks group on the Tasks ribbon.
18. Click Tasks in Quick Launch.
19. The new task is self assigned to the user.


Team Details section.