Same content mean that all the records or the MySQL table must be identical.
For the user, you need that user id 1 means exactly the same in all the websites.
This is the same for the sessions.
If you want to remain logged, you need to share the session and the user information.
When user id 1 mean "john" on site A, it MUST also mean "john" on site B.
So record id = 1 must be identical.
To do that, you need to share the MySQL tables.
If you want to simplify the setting, you can use JMS that is providing the facility to share the users.
Otherwise ask you MySQL administrator to help you creating manually the sharing of the mysql table.
I already explain that you have to use the MySQL create view command.
You need to to that for all the #__users% table and also for the #__sessions
If you are not a technical guy and that you want that we do it for you in your server, we also have a billable support that you can order at
www.jms2win.com/en/joomla-multisite?page...35&category_id=1