...As regards that map, it's sorta
related to what goes on onscreen. About as related as I'm to Abraham Lincoln, but still.
The map is the handiwork of a fan named Christian Rühl, and attracted the attention and approval of another fan Geoffrey Mandel who then wrote and illustrated the Star Trek Star Charts
book. The book isn't canon - but was in turn an influence on the people who made DS9 and VOY, and some of its artwork in fact was created in two-way cooperation with those people and shows.
No, this chain of events does not
establish the relative sizes of the UFP, the RSE and the KE in canonical terms. But amusingly enough, it does establish things like the route of the Voyager
: the canonical route map, glimpsed in some Season 7 episodes, was a Mandel piece first portrayed in this book. (Alas, this galactic map doesn't show such fine detail as the tiny dots that would be UFP, RSE and KE...)