In the Disney canon wiki page of the New Republic, it is described that following the Battle of Jakku, the Empire was militarily exhausted and forced into signing a peace treaty with the Republic. Imperial forces thereafter stayed within the borders defined in the treaty. This indicates that the Galactic Empire and New Republic likely coexisted for an extended period - until the Empire probably fractured with infighting, eventually leading to the rise of the First Order to be seen in The Force Awakens.
As of the ratification of this peace treaty, what are the established territories and borders of the two galactic governments, as far as what is known to us - named worlds, sectors etc.? Are there areas of the galaxy that fall outside both governments, and how much of these "neutral space" were formerly controlled by Palpatine's Empire and how much were neutral since before the Empire? Please answer strictly within Disney canon.