Minimum Size of Pressure Canners
The smallest physical size of pressure canner that the National Center for Home Food Preservation and the USDA are willing to call “canners” are pressure canners that can hold a minimum of 4 x 1 litre (US quart) jars.
This seems to translate into an advertised total internal volume for the canner of 10 quarts. All American offers a 10-quart size for sale as a canner which they say will hold 4 x 1-quart jars. All-American won’t support this small a size for canning fish, though. More info here. Some other makers offer 12 quart pressure canners holding the required minimum 4 jars. For information, see Pressure Canner brands. To be clear, no reputable source says the minimum size pressure canner is 16-quarts; rather, they all have been saying, “must hold 4 quart jars”, and that is very different.
Though some people may attempt to do canning in smaller sized pots in the “pressure cooker” range, what they produce is not regarded as safe for consumption by the USDA, and the pots they use are regarded as pressure cookers, not large enough to graduate up to the term of “pressure canner.”
Today’s marketplace offers a variety of smaller pressure-based cookers/canners. Retort size has the potential to affect come up and cooling rates, which contribute to the sterilizing value of a pressure process. As heating and cooling times are reduced so is total lethality. ……. The majority of the lethality was achieved during cooling. …. Home canning in very small retorts should be avoided until safe process recommendations can be determined.”  R.J. Pakola and E.L. Andress. Heat Penetration Studies of Stewed Tomatoes in 6, 8, and 17 Quart Household Pressure Retorts. Paper 46B-7. Presented at the Institute of Food Technologists Annual Meeting Anaheim, CA, June 17, 2002. Accessed March 2015 at https://nchfp.uga.edu/papers/2002/heatpenetration.html
To be considered a pressure canner for USDA processes, the canner must be big enough to hold at least 4 quart-size jars. Pressure cookers/saucepans with smaller volume capacities are not recommended for use in canning. Enough heat may not be delivered during pressurizing and the cool-down period in smaller pressure cookers/saucepans.”  Andress, Elizabeth L. Pressure Canning and Canning Low Acid Foods at Home. Cooperative Extension: University of Georgia. Powerpoint presentation, slide 20. Accessed March 2015 at nchfp.uga.edu/multimedia/slide_shows/CanLowAcid_web08.ppt.
To use the USDA canning procedures, make sure you select a pressure canner/cooker that is capable of holding at least 4 quart size jars, on the rack, with the lid in place ready to can. If it is smaller than that, we do not recommend it for home canning.” Andress, Elizabeth L. Can Your Vegetables Safely. June 2010. Accessed March 2015 at https://nchfp.uga.edu/tips/summer/can_vegetables_safely.html
For more information, see Pressure Cookers versus Pressure Canners.
Exceptions to minimum size recommendation
The University of Wisconsin Extension Service sets the minimum size not by a minimum number of jars that a pressure canner can hold, but rather by the overall volume capacity of the canner:
Use only a larger 16- to 22-quart pressure canner. Safe processing times have not been determined for smaller pressure canners.”  Ingham, Barbara H. et al. Canning Meat, Wild Game, Poultry & Fish Safely. University of Wisconsin Extension Service. Wisconsin Safe Food Preservation Series. B3345. 2002. Page 9.
(Mind you the wording almost implies that they don’t want you to use canners larger than 22-quart, which presumably is actually not the case.)
Smoked fish exception
The maker of All American pressure canners recommends against using its two smallest pressure canners (10.5 quart and 15.5 quart) for home canning smoked fish:
“The 10.5 Qt Model 910 and 15.5 Qt Model 915 are NOT suitable for canning smoked fish.” All American web site. http://www.allamerican-chefsdesign.com/Product-Detail.asp?iBrand=1&hProductType=10 and http://www.allamerican-chefsdesign.com/Product-Detail.asp?hProduct=33
“Smoked Fish: ….Use a 16 quart or larger pressure canner for this procedure; do not use smaller pressure canners. Safe processing times haven’t been determined.” All American Manual. 2014. Page 35.
16 quart size limitations
16 quart sizes of Mirro and Presto have the same width as their larger (22 and 23 quart, respectively) sizes. What they are missing is the height of the larger sizes. Consequently, you can’t double-deck half-litre (US pint) jars in them. Nor can you water bath process 1 litre (1 US quart) jars in them, simply because you can’t cover the jars with 2 to 3 cm (1 inch) of water and get it to boil without boiling all over the stove: they are just that little bit too short for that.
This size, however, has the advantage of being faster than the larger canners: faster in heat up and faster in cool down, proving that sometimes smaller is just a better fit.
When too big is too big
If you use a canner too big for the job at hand, for instance a 41 quart canner to process 4 x half-litre (US pint) jars of green beans, that is perfectly fine: there is no risk to safety or food quality. It’s just a question of energy efficiency. You will be using more energy than needed to fire up and run that huge canner, increasing your energy cost per jar and increasing your carbon footprint. Many home canners want to reduce their costs of living, or reduce their carbon footprint, or both.
It’s nice to have flexibility.
Should you get the canning bug and find that you can justify the need for a second pressure canner, you may wish to consider arranging it so that you have two different sizes. Say, a 16 quart, and a larger one such as 23 and up. The 16 quart becomes the one you use for smaller loads, or overflow, while the 23 quart (or higher) becomes the workhorse that handles the big loads.