  We present the Synthetic UniveRses For Surveys ({\sc surfs}) simulations, a
set of N-body/Hydro simulations of the concordance $\Lambda$ Cold Dark Matter
(\LCDM) cosmology. These simulations use Planck cosmology, contain up to 10
billion particles and sample scales & halo masses down to $1~$kpc & $10^8{\rm
M}_\odot$. We identify and track haloes from $z=24$ to today using a
state-of-the-art 6D halo finder and merger tree builder. We demonstrate that
certain properties of halo merger trees are numerically converged for haloes
composed of $\gtrsim100$ particles. Haloes smoothly grow in mass, $V_{\rm
max}$, with the mass history characterised by $\log
M(a)\propto\exp\left[-(a/\beta)^\alpha\right]$ where $a$ is the scale factor,
$\alpha(M)\approx0.8$ \& $\beta(M)\approx0.024$, with these parameters
decreasing with decreasing halo mass. Subhaloes follow power-law cumulative
mass and velocity functions, i.e. $n(>f)\propto f^{-\alpha}$ with
$\alpha_{M}=0.83\pm0.01$ and $\alpha_{V_{\rm max}}=2.13\pm0.03$ for mass \&
velocity respectively, independent of redshift, as seen in previous studies.
The halo-to-halo scatter in amplitude is $0.9$~dex. The number of subhaloes in
a halo weakly correlates with a halo's concentration $c$ \& spin
$\lambda$:haloes of high $c$ \& low $\lambda$ have $60\%$ more subhaloes than
similar mass haloes of low $c$ \& high $\lambda$. High cadence tracking shows
subhaloes are dynamic residents, with $25\%$ leaving their host halo
momentarily, becoming a backsplash subhalo, and another $20\%$ changing hosts
entirely, in agreement with previous studies. In general, subhaloes have
elliptical orbits, $e\approx0.6$, with periods of $2.3^{+2.1}_{-1.7}$~Gyrs.
Subhaloes lose most of their mass at pericentric passage with mass loss rates
of $\sim40\%$~Gyr$^{-1}$. These catalogues will be made publicly available.
