Where does the Sahara stop ?

As I mentioned in another blog , I had the opportunity to attend a roundtable about the Sahara at Georgetown University in Washington, D.C. A delegation of Sahrawis presented to a small audience the idea of an autonomy project for the Sahara region. The proposal is destined to the King of Morocco. The delegation leader, named Khalihenna, gave an interesting insight about the Western Sahara issue.
He explained how Sahrawi tribes have lived and still live in Algeria, Mali, Mauritania and Morocco. I don't remember if he mentionned Chad also.
It's an interesting data to consider when studying the subject : does the revendication for an independent country in the Sahara include all the Sahara region (from the Atlantic to Chad) ? Until now, I know only of revendications regarding the Moroccan territory.
I know some Sahrawis who have mauritanian citizenship and have family members deeply integrated both in Morocco and in Mauritania. I wonder how do they look at the Sahara issue.