Now the question is; Are you the leader of New Vegas? Or simply make it 'free' by allowing the citizens of New Vegas to choose what they want? Since it is seen by your own conversations(Asking Yes Man; "What if I wanted to take Vegas for myself" or at the end when confronting Gen. Oliver Lee and claiming "The Republic has outstayed its welcome - This land is mine", And if you do get the Speech on the General he doubts you have the guts to 'train troops, make supply trous, form cities", etc) it would be referenced that you do take Vegas for yourself as its new Overlord of evil or its benevolent (insertleadernamehere). Although in the ending it is also referenced in some dialoge that you dont seem to control Vegas.
(At Arcades ending where he stays put in Freeside he "teaches the locals to govern themselves" though in the ending where he magically participates in the battle for the Dam he "maintains order". There's also the FotA ending where they claim that you have brought ruin on them just because you wanted an Independent New Vegas.)
The only other refernece to a 'chaos enduced Mojave'(Even though you have a Mark II Securitron army at your disposal and perhaps numerous allies) is in the Boomers ending. Though I can't see why they wouldn't help you maintain Order since you basically made their destruction-filled fantasy come true.
Any ideas?