Have made a couple of sopranino/ piccolo Ukes with 27 cm (11") scales and have been tuning them with reentrant dgbe high tuning (an octave above a 4 string standard guitar but a uke style higher d string. In terms of playing this effectively makes them a half scale guitar with a no change required to fingering for guitar players. The half scale guitars I see like the yamaha Guitalele have a 433 mm (17") scale which is akin to a tenor or baritone Uke. Other "half size" guitars I saw on ebay had 20" scales. A standard guitar has a scale length of closer to 650mm (26").
To improve the playability of the sopranino Ukes I splurged $4 on a roll of 30lb fishing line so I am now stringing them up with a 40 60 50 30 lb mix rather than standard & tenor ukes which I had been stringing up with 50 80 60 40 lb line. The shorter line makes for a harder bend so a thinner guage makes them easier to play.
How can people call these big things half size? Is a sopranino uke really a half size guitar?
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1/2 and 3/4 size musical instruments are conventional rather than literal nomenclatures. If you look at a 1/2 size classical guitar or violin, you will see that it is somewhat smaller than a "full size" but not physically half the size. The same goes for double bases, most of them are "3/4 size" with a scale length of about 41" as opposed to full size which is around 43".