In op-amp, how do they remove Quiescent votage (bias voltage of a bjt) from the output?
This can be done with level shifting and requires a bipolar power supply.  The simple sketch below illustrates this, showing only the components pertinent to this concept.  

The collectors of the first differential pair (Q1 &amp; Q2) are as you described in your question...biased above 0V.  The second differential pair (Q3 &amp; Q4) uses PNPs and its output is biased down to just above 0V.  This is buffered by the emitter follower, Q5.  I showed it fed back to the (-) input of the amplifier simply to illustrate the path for negative feedback.   







simulate this circuit &ndash; Schematic created using CircuitLab