Prepare the boiling-water canner, jars and lids.
Wash, peel, core and slice the apples.
Place the apples in a large, heavy-bottomed stockpot with ½ cup water.
Cook over medium heat, stirring frequently, until the apples are completely tender. This will take approximately 5 to 20 minutes.
Run the softened apples through a food mill for smooth applesauce, or mash them for a chunkier sauce.
Return the applesauce to the pot and bring it to a boil, stirring frequently to prevent scorching.
Ladle the hot applesauce into hot jars, leaving ½ inch of headspace.
Remove air bubbles and check the headspace again.
Wipe the jar rims, center the lids and apply the bands fingertip tight.
Process pints for 15 minutes and quarts for 20 minutes at elevations up to 1,000 feet. Adjust the processing time for elevation using the chart above.
When the processing time is complete, turn off the heat and remove the canner lid. Wait 5 minutes before removing the jars.
Cool the jars undisturbed for 12 to 24 hours. Check the seals, remove the bands and label the jars before storing.