I can't post the schematic from this phone
http://electronics-diy.com/electronic_schematic.php?id=116

My question is the offset DC output.
Notice the IC'S are tied to a separate ground. Seems to be held by a zener?
Or is the resistor/capacitor in the AC leg and diode D6? making a separate halfwave rectifier. (Transformerless mains connection possible, but let's not go there yet)
Are they doing something "chinese" with the AC input to get them to a zero to whatever power supply that answers the 1.2 volt offset problem like the one going on in another thread right now?

 

That supply is a true "zero" volt capable supply. They aren't doing anything weird - the ICs are opamps (U2, anyway) that compare the output off R12 to the voltage provided by P1 and forces the output pass transistors to match the voltage shown on P1.

The circuit in which D7 resides provides a slight negative supply voltage so that the opamps can truly output "zero" volts.

 

The "network" where D7 resides is a charge pump that provides negative voltage (as said by @SLK001 ). I used it in a simple project to feed the regulation terminal of a LM317 (notoriously starting from 1.25 volts). Feeding it with a negative voltage of -1.25 volts it starts its output at 0 volt. Some trimming (or better, a stable, negative -1.25V vref) and "les jeux sont faites".