See below a self-power supply design I took from a App Note from Texas Instruments.

My question is about the voltages at the inputs of the comparator U6A. At the inverting input, the reference is set to 0.7 V because of the diode D12, right? At the non-inverting input, the voltage is defined by the resistor R41//R42. If the voltage across C27 increases, the voltage drop across R41//R42 will increase so triggering the comparator. Am I right? In addition, what's the purpose of C34 in parallel with R43 at the comparator's output?

 

The Voltage across the supply will have to be over 39.7V to trigger the Zener on pin 3 of the U6a, the capacitor C34 is to assist fast turn off for the fet.