Why are there no A or B sized batteries ?

They were REALLY big! I forgot about those, they were used in radios before transistors came along.

There's a picture of an A, B, and C (via links) here: http://en.wikipedia.org/wiki/A_battery_%28vacuum_t...

Real batteries (made out of more than one cell) ... nowadays most "batteries" are really single cells.

In electronics, an A battery is any battery used to provide power to the filament of a vacuum tube. It is sometimes colloquially referred to as a "wet battery" (although there's no reason why a "dry" battery of suitable voltage couldn't be utilised for the purpose) The term comes from the days of valve (tube) radios when it was common practice to use a dry battery for the plate (Anode) voltage and a rechargable lead/acid "wet" battery for the filament voltage.

B battery is any battery used to provide the plate voltage of a vacuum tube. It is sometimes colloquially referred to as a "dry battery" (although there's no reason why a "wet" battery of suitable voltage couldn't be utilised for the purpose) The term comes from the days of valve (tube) radios when it was common practice to use a dry battery for the plate (Anode) voltage and a rechargable lead/acid "wet" battery for the filament voltage.

Even when the plate voltage rail is fed by a power supply rather than a battery, it is generally referred to as the "B+" line.

C battery is any battery used to provide bias to the control grid of a vacuum tube. Until the early 1930s this was common practice in valve (tube) radio sets but was largely superseded by grid leak resistors or voltage divider biasing

Well this is a good question and you have really look close at the history of the battery. First i really have no idea.