Predicting the spatial distribution of objects as a function of cosmology is
an essential ingredient for the exploitation of future galaxy surveys. In this
paper we show that a specially-designed suite of gravity-only simulations
together with cosmology-rescaling algorithms can provide the clustering of dark
matter, haloes, and subhaloes with high precision. Specifically, with only 3
$N$-body simulations we obtain the power spectrum of dark matter at $z=0$ and
$z=1$ to better than 3\% precision for essentially all currently viable values
of 8 cosmological parameters, including massive neutrinos and dynamical dark
energy, and over the whole range of scales explored, 0.03 < $k/h^-1Mpc$ < 5.
This precision holds at the same level for mass-selected haloes and for
subhaloes selected according to their peak maximum circular velocity. As an
initial application of these predictions, we successfully constrain
$Ømega_m$, $\sigma_8$, and the scatter in subhalo-abundance-matching
employing the projected correlation function of mock SDSS galaxies.