When you create a new distribution list, the default setting is that the list is shared with no one and can be edited by only you. However, you can designate which Admins you want to have access to the list and which ones can edit the list.
To share an existing list, select the list from your contacts page and click the "Manage List" drop down menu.
After adding the Admin, you can check to box labeled "Can Edit" if you would like for them to be able to edit the list as well. By giving someone the ability to edit a list, they can change the title of the list, add and remove people from the list and even share the list with others.
After clicking "Save" your new changes will be saved and your Admins will see the list appear among their other distribution lists. They will also receive an email notification that they now have access to this list.