Thiessen map

By calculating a Thiessen map, each pixel is assigned the class name, ID or value of the nearest source.

A Thiessen map can be created by performing a Distance calculation on any raster source map. In the Distance calculation dialog box, a source map can be any raster map with a class domain or an ID domain. On the command line, you can also use raster maps with a value domain. A weight map can be used but is not obligatory.

If your sources are points, and you do not want to take accessibily factors into account, the best way to create a Thiessen map is to use the Nearest point operation.