  We perform a sequence of binary black hole simulations with increasingly
small mass ratios, reaching to a 128:1 binary that displays 13 orbits before
merger. Based on a detailed convergence study of the $q=m_1/m_2=1/15$
nonspinning case, we apply additional mesh refinements levels around the
smaller hole horizon to reach successively the $q=1/32$, $q=1/64$, and
$q=1/128$ cases. Roughly a linear computational resources scaling with $1/q$ is
observed on 8-nodes simulations. We compute the remnant properties of the
merger: final mass, spin, and recoil velocity, finding precise consistency
between horizon and radiation measures. We also compute the gravitational
waveforms: its peak frequency, amplitude, and luminosity. We compare those
values with predictions of the corresponding phenomenological formulas,
reproducing the particle limit within 2%, and we then use the new results to
improve their fitting coefficients.
