Howdy,

the question is quite simple. What's a floating regulator and how is it designed?.

I'm looking for some basics.

 

Look here: http://www.k7mem.150m.com/Electronic_Notebook/power_supplies/lm317.html

The maximum voltage difference that an LM317 "sees" is from it's ADJ terminal to its' IN terminal. It adjusts the current output in an attempt to keep Vref (the difference between the OUT terminal and ADJ terminal) at a nominal 1.25v.

If you're wondering about "isolated" regulators, that's a different topic altogether.