Wash and cut the tomatoes. Check each fruit, cut out any blemishes or moldy spots. Cut the tomatoes lengthwise in quarters.
Put the tomatoes through a strainer – follow the directions for the one you have. I use an attachment for a KitchenAid stand mixer. Extract the most pulp that you can.
Put the tomato pulp into one or more large slow cookers. Set the cookers on high and cook, covered, for 1-2 hours.
At the end of that time, check that the tomato pulp is hot and bubbling around the edges. Now prop the lid with chopsticks or wooden spoons, so that there's about a half inch of airspace. This permits evaporation.
Cook for 24 hours or so. Stir occasionally if you'd like. When you can dit all the pulp into one slow cooker, feel free to do that. If the texture of the tomato pulp is a bit lumpy, whiz it with an immerzion blender to make it smooth.
Continue cooking with the lid propped open until the tomato paste is thick and uniform. Test it: if a spoonful plopped on a saucer does not separate, and retains its shape, it's done.
Ladle the tomato paste into prepared 4-oz jars, leaving ½ inch headspace. While I prefer the smaller jars, the National Center for Home Food Preservation says you may can tomato paste in (at largest) 8-oz jars. Add citric acid to each jar: ⅛ teaspoon for 4-oz jars, and ¼ tsp for 8-oz (half pint) jars.
Place lids and bands on jars. Process in a boiling water bath 45 minutes (the time is the same for 4-oz and 8-oz jars.)
Let cool, label, remove bands, and store in a dark place.
I like to take some of my tomato paste and freeze it in a silicon ice cube tray. It's so very handy to have a bit of paste to use as needed. A standard ice cube tray's wells hold roughly 2 tablespoons.