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You mean 3 transistors?... I hope you have a link for its pic.
I am sure, the circuit of interest is simple and clear to you but to those who have seen thousands of circuits, it is hard for them to be 100% sure of all its details from your description.
Sorry... perhaps some others have a better idea of it.
* The darlington pair works like a single transistor with h21=h21,1*h21,2 but with an overall transconductance g=0.5*g2.
Transconductance g2 (2nd transistor) is determined by Ic,2. (Very often, this is forgotten believing that a high current gain automatically leads to high voltage gain)
* two emitter stages allow more voltage gain. I am not sure if the buffer in between makes really sense.