In MeisterTask, tasks are either unassigned, or assigned to one specific project member, ensuring a clear distribution of responsibilities. Other project members interested in receiving updates about a task are able to add themselves as 'Watchers' to the task.
When a task is assigned to a user, their avatar appears in the upper right corner of the task tile, so you can see at a glance who owns which task while looking at your project board.
You can assign a task both from the project board and from within the task dialog:
Assign Task from the Project Board
Simply hover over the right top corner of an unassigned task and click on the question mark to open the member list. Click on the avatar or name of a user to assign the task to them.
Assign Task from the Task Dialog
The currently assigned person is always shown at the top of the task dialog. Click on Unassigned to open the member list. You can click on the avatar or name of a user here as well to assign the task to them.
You can easily show all tasks of one assignee by clicking on their avatar in the members bar on the right side of the project board.