Push pull CMOS output stage overcoming the distortion problem
1.) The transistors M4 and M5 act like a floating voltage source. M3 is a current source and therefore the voltage across M4 and M5 is constant.

M6 and M3 form a common-source stage that allows to move the floating voltage source up and down. This eliminates the region where neither M1 nor M2 is conducting, therefore distortion is reduced.

2.) All these transistors should be in saturation. M4, M5 will always be in saturation since they are diode-connected.

3.) The dimensioning is usually done for the quiescent condition where the output signal is zero. For this case M4/M1 and M5/M2 act like current mirrors.

The ratio determines the quiescent current.