A question about frequency compensation

I see in many 1980s and 1990s 's op-amps used nested Miller compensation .

A capicitance is connected between the one output of input differential stage
and the output of the opamp , and one other capicitanc is connected
between the output of the one output of the second stage .

What confused me is there always another capicitance was connected between the other output of the first differential stage and the VDD or VSS .

So my question is what is the effect of this capicitance and wheather this capicitance generate the first non-dominidant pole , and if so , wheather the
bandwidth is decreased by this capicitance ?

Added after 2 minutes:

I really hope some one can help me . I post many topic in
this forum , but I find there is no one can really give me
an useful answer . I hope this time some one can give me
real help

The capacitance of first output opamp to supply voltage rail is a signal path to ground. The effect of this capacitance maybe compensated (like pole-zero) by the capacitance between output and input of second stage.