  In this paper, we develop a theory on the degenerations of Blaschke products
$\mathcal{B}_d$ to study the boundaries of hyperbolic components. We give a
combinatorial classification of geometrically finite polynomials on the
boundary of the main hyperbolic component $\mathcal{H}_d$ containing $z^d$. We
show the closure $\overline{\mathcal{H}_d}$ is not a topological manifold with
boundary for $d\geq 4$ by constructing self-bumps on its boundary.
