A map owner or manager can change who the diagram owner and author is. By default, the map owner is set as the owner and author for each process diagram in the map. However, if you want to manage responsibility between users, you can do it on the diagram's right panel. Just click "change" against either owner or author.
You will see a dialog window where you can start typing the name of the user you wish to make the new owner or author.
you can make any user in your space a process owner
you can make any editor in the space a process author