Blank map of New Hampshire
All 10 counties, unlabeled and unfilled. The SVG prints at any size without going fuzzy and opens in any editor. It comes out taller than it is wide, so it prints upright.
What you are printing
A conic projection centered on New Hampshire, so the counties keep their shapes instead of leaning the way they do on a world map.
Every county is a separate shape, so a vector editor can select and fill one without touching the ones around it. Names are in the file as titles rather than as drawn text, which is what keeps the printed sheet blank.
Every county on it
The map page lists all 10 counties by name, and colors them in the browser if you would rather not print anything.