INDIANAPOLIS — N.C.A.A. member schools and conferences voted Thursday to adopt a new, stripped-down constitution, the first step in decentralizing an organization that faces increasing challenges to its relevancy as the chief authority in college sports.

But the debate over the association’s passage of the new charter, which will empower schools and conferences, hinted at the increasingly stark divide between the mission and financial might of those thousands of varied institutions — from football powerhouse like the national champion Georgia and nonscholarship athletes at places like Grinnell College.

That gap promises to be central as the N.C.A.A.’s three divisions hash out details of how they will overhaul themselves in the coming months.