  It is well known that the bounding curve of the central hyperbolic component
of the Multibrot set in the parameter space of unicritical degree $d$
polynomials is an epicycloid with $d-1$ cusps. The interior of the epicycloid
gives the polynomials of the form $z^d+c$ which have an attracting fixed point.
We prove an analogous result for unicritical Blaschke products: in the
parameter space of degree $d$ unicritical Blaschke products, the parabolic
functions are parameterized by an epicycloid with $d-1$ cusps and inside this
epicycloid are the parameters which give rise to elliptic functions having an
attracting fixed point in the unit disk. We further study in more detail the
case when $d=2$ in which every Blaschke product is unicritical in the unit
disk.
