Hi,
This was going to be a question, but in the end I found it... So I'm posting a clear message as all the others on the subject either refer to installed Jira, or don't actually say where to do this.
1) as it's mentioned everywhere, turn ON the option "Allow unassigned issues"
go to the Cog icon at the top right of myproject.atlassian.net, pick "System", the page title is "General Configuration" (I never understand web sites that have menu items not matching the title of the page). In the "Options" section half way down, you'll find "Allow unassigned issues". Turn it ON.
2) To change the "Default Assignee"...It took me ages to find this...
go to the Cog icon at the top right, pick "Projects Admin", then click on your project name in the list (alternatively, when in your project, click the "Administer Project" button at the top right of the page). Pick "Roles" in the left menu. Hidden in the blurb at the top of the page, just under "JIRA enables you to allocate particular people ....." you will find "Project Lead" and "Default Assignee" with a little Edit icon next to it. That's it !
What is confusing is that if you click on the Cog/"Projects Admin", you see a list of project with the column "Default Assignee" and "Project Lead", but the Edit button on that row doesn't let you change those values. It's quite unintuitive.
Combined with the fact that lots of help pages say "Go to the 'General Configuration' page" and there is not a single menu item called by that name.... it's making it very hard to find things in a very complex system.