I've personally seen giants over four inches. But they weren't particularly well-formed. I had a 3 incher (nose to caudal peduncle) from Petco who died of ammonia from having been kept in one of those small cups.
My avatar picture is my giant plakat, 2.5in BO (body only) and growing, who succumbed to bad digestion (swim bladder?) in less than a day.
Some of the early giants were over four inches (some say five). But, when they were back-bred for looks, finnage and color, naturally they became smaller. Now Thai breeders call anything over 2in BO a giant. They call those 2.5in fish. Stone is right in his observations there.
More than absolute size, a giant is determined by genetics. So a 2in standard Betta is not a giant. But a 1.8in giant is.
Someone mentioned growth hormone. There really is no reliable growth hormone, even for commercial farm-raied fish, let alone pet fish. However, there is an anti-growth hormone, called a "stunting hormone" exuded by fry in an attempt to keep their sibling small and less competitive. A good giant breeder separates his fish as soon as possible to keep this from happening.
So, really, there is no such thing as a half-giant. The breeders are just doing their best to breed large, attractive Betta fish. Some are just bigger and better than others.
Hey, Edgy, here's a pic of Setsuna's wild B. splendens. See any similarity?