Thiessen Polygons

Thiessen Polygons (also known as Voronoi or Dirichlet cells) are Polygons created automatically based on selected items. Adjacent Polygon items are created whose boundaries are equidistant from the selected items.

Thiessen Polygons are created as Polygon items on the current overlay.

Ensure the overlay on which you want to create the Thiessen Polygons is the current overlay (you could consider creating a separate overlay for these items).
Select the items around which to create areas of influence. There must be at least two of them.
Select Analysis > Buffer > Thiessen Polygons.

Example:

A city is holding elections. There are many polling stations where people can walk to vote. Each house must be allocated to a polling station but you need to ensure each house is allocated to the closest one.

To do this:

Create a Point item at each polling station.
Select the polling stations.
Use Thiessen Polygons to create the Thiessen Polygons. This will give you the Polygon (area) which each polling station will collect voters from.
For each Polygon, use Home > Selection > Find to find all the houses inside that area.

Editing Thiessen Polygons

Once constructed, a Thiessen Polygon can be edited in the same way as any Polygon item - you can change its size and shape, its pen and brush etc.