Transistors and darlingtons have a wide range of base-emitter voltage that also changes as they get warm. The datasheets show a maximum voltage for some of them and a typical voltage for others but the range is so wide that you will need to test the one you use and calculate a resistor for it. Your idea of using a 100mA regulator and 1900mA in the pass transistor makes selecting the transistor and calculating the resistor a nightmare. The circuits I showed use a normal 1A regulator with about 600mA in it and a pass transistor with a few Amps. Then any minimum or maximum transistor will work and calculating the resistor value is easy.
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