Sorry but this is an awfull circuit - dont build it!
Let us assume a specification of 0 to 12v, 1 amp max.
The circuit as drawn will only ever give a maximum of about 9.2 volts
zener (voltage 20 volts), divided by 2 (the two 5k resistors), minus the Vbe of the transistor (about 0.6 to 0.8 volts) = 9.2 volts.
If you try to take 1 amp from this circuit, the 25ohm 1 Watt resistor will drop 25 volts, and get very hot (W= VxI) it will dissipate 25 watts for a short while until it bursts into flames.
The output voltage will be variable, you can adjust it with the 5k variable resistor, but no way could it be described as regulated.
As you take current from the output, base current will flow in the transistor and the voltdrop through R3 and R4 will increase, the voltage at the base of the transistor will drop and so will the output voltage.
There is no feedback to give any regulation.
This circuit has NOTHING to commend it.
If you have an LM317, look here
**broken link removed**
download the datasheet and look at page 16 for a regulator circuit which can turn down to zero.
JimB