Abstract: 
This is a continuation of the work [Ba] dealing with the
family of all cubic rational maps with two supersinks. We prove
the existence of the following parabolic bifurcation of
Mandelbrot-like sets in the parameter space of this family.
Starting from a Mandelbrot-like set in cubic Newton maps and
changing parameters in a continuous way, we construct a path of
Mandelbrot-like sets ending in the family of parabolic maps with
a fixed point of multiplier $1$. Then it bifurcates into two
paths of Mandelbrot-like sets, contained respectively in the set
of maps with exotic or non-exotic basins. The non-exotic path
ends at a Mandelbrot-like set in cubic polynomials.

1. Institute of Mathematics
   Warsaw University
   Banacha 2
   02-097 Warszawa, Poland