The bounds of the output map are limited by the current region (see g.region).
The -a flag can be used to create a Voronoi diagram for areas.
The -s flag can be used to extract the center line of areas or skeletons of areas with thin >= 0. Smaller values for the thin option will preserve more detail, while negative values will extract only the center line.
Voronoi diagrams may be used for nearest-neighbor flood filling. Give the centroids attributes (start with v.db.addcolumn), then optionally convert the result to a raster map with v.to.rast.
The extraction of skeletons and center lines with the -s flag is a brute force approach. Faster and more accurate algorithms to extract skeletons from areas exist but are not yet implemented. In the meantime, skeletons and center lines can be simplified with the Douglas-Peucker algorithm: v.generalize method=douglas.
g.region -p raster=elev_state_500m v.voronoi input=hospitals output=hospitals_voronoi
g.region -p n=162500 s=80000 w=727000 e=846000 res=500 v.voronoi input=urbanarea output=urbanarea_voronoi -a
g.region -p n=161000 s=135500 w=768500 e=805500 res=500 v.voronoi input=urbanarea output=urbanarea_centerline -s v.voronoi input=urbanarea output=urbanarea_skeleton -s thin=2000