  This is a continuation of notes on dynamics of quadratic polynomials. In this
part we transfer the our prior geometric result to the parameter plane. To any
parameter value c in the Mandelbrot set (which lies outside of the main
cardioid and little Mandelbrot sets attached to it) we associate a ``principal
nest of parapuzzle pieces'' and show that the moduli of the annuli grow at
least linearly. The main motivation for this work was to prove the following:
  Theorem B (joint with Martens and Nowicki). Lebesgue almost every real
quadratic polynomial which is non-hyperbolic and at most finitely
renormalizable has a finite absolutely continuous invariant measure.
