We characterize the revenue maximizing allocation mechanism for a risk neutral seller that owns N , possibly heterogeneous, objects and faces I risk neutral buyers with very general preferences, which allow for complements, substitutes and externalities. Buyers care about the entire allocation of the objects, even if they do not win any, so the auction outcome may a¤ect them also when they do not to participate, and these non-participation payo¤s may very well depend on their type. The main novel message of our analysis is that with type-dependent non-participation payo¤s, the revenue maximizing assignment of objects can crucially depend on the outside options that buyers face. Outside options can therefore a¤ect the degree of e¢ ciency of revenue maximizing auctions. We show that sometimes an optimal mechanism will allocate the objects in an ex-post e¢ cient way, and other times buyers will obtain objects more often than it is e¢ cient. Our characterization rings a bell of caution. Modeling buyers' outside options as being independent of their private information, is with loss of generality and can lead to quite misleading intuitions.