  In the space $\mathbb{C}$ of the parameters $\lambda$ of the unicritical
polynomials family $f(\lambda,z)=f_\lambda(z)=z^d+\lambda$ of degree $d>1$, we
establish a quantitative equidistribution result towards the bifurcation
current (indeed measure) $T_f$ of $f$ as $n\to\infty$ on the averaged
distributions of all parameters $\lambda$ such that $f_\lambda$ has a
superattracting periodic point of period $n$ in $\mathbb{C}$, with a concrete
error estimate for $C^2$-test functions on $\mathbb{P}^1$. In the proof, not
only complex dynamics but also a standard argument from the Nevanlinna theory
play key roles.
