Ernest Ka'ai was the Ukuleles first superstar. He is most famous for his playing and teaching, (he wrote the first how to play the Ukulele book in 1906 and invented a lot of the notations and chord diagrams that are seen today), and in 1909 he started the Ernest Ka'ai Manufacturing company making Ukuleles. 

In 1917 he sold the company and bought shares in the Aloha Ukulele Manufacturing co. but the Ernest Ka'ai factory carried on without him for another three years. I have seen Ukuleles that don't have a Spanish heel and a wooden round bodied model both looking mainland made but bearing the Ka'ai headstock logo? As far as I can find out they were made in the Ka'ai factory in Hawaii. 

What I don't believe is the case though is that the Larson Brothers, (as sugested elsewhere), had anything to do with the Kaai enterprise. They spent all of their working lives in Chicago and though famous for Guitars and Mandolins don't seem to have made many Ukuleles. I also think the numbers after "Special" on the sound hole labels is a serial number and not a date.