>>I don't know what you mean by Member.Session (?) but yes, ASP.NET session.
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>The Member.Session field is a framework related field I am using to recognize the user from a stored cookie. That is initialized at login.
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>>Yes. If you allow sessionId to be stored in a cookie you will get the same id for new instances (or new tabs) for the relevant browser.
>>If 'cookieless=true' the session id is included in the URL and you get a different session for each instance or tab.
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>Is this something you have to maintain on your own or this is all automatic?

Should be automatic. Also, for example, links from a page will add the same SessionId to the link....