It isn't an efficient design but as Chukey said, you must be careful to use distilled water and ensure nothing can dissolve into it or you will get corrosion and electrolytic effects.
Chuckey, it's operation is quite simple: the 7812 provides all the output curent until enough voltage is dropped across R7 to start forward biasing the power transistors. They then carry any additional current. It has the advantage that the voltage across R7 is proportional to the output voltage when under load so the regulator controls the transistors as well and it's thermal shutdown also shuts the transistors off. However, in this schematic, R7 at 100R is FAR too high in value, it should drop Vbe (say 0.7V) at about 75% of the 7812's maximum current. If we say that is 750mA, it's value should be V/I = about 0.9 Ohms. In fact f the DC from the rectifiers is ~34V it is only possible for the 7812 to conduct a maximum of 0.34A so the 1A fuse can never blow.
Brian.