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We present the novel algorithmically regularised integration method MSTAR forhigh accuracy ($|\Delta E/E| \gtrsim 10^{-14}$) integrations of N-body systemsusing minimum spanning tree coordinates. The two-fold parallelisation of the$\mathcal{O}(N_\mathrm{part}^2)$ force loops and the substep divisions of theextrapolation method allows for a parallel scaling up to $N_\mathrm{CPU} = 0.2\times N_\mathrm{part}$. The efficient parallel scaling of MSTAR makes theaccurate integration of much larger particle numbers possible compared to thetraditional algorithmic regularisation chain (AR-CHAIN) methods, e.g.$N_\mathrm{part} = 5000$ particles on $400$ CPUs for $1$ Gyr in a few weeks ofwall-clock time. We present applications of MSTAR on few particle systems,studying the Kozai mechanism and N-body systems like star clusters with up to$N_\mathrm{part} =10^4$ particles. Combined with a tree or a fast multipolebased integrator the high performance of MSTAR removes a major computationalbottleneck in simulations with regularised subsystems. It will enable the nextgeneration galactic-scale simulations with up to $10^9$ stellar particles (e.g.$m_\star = 100 M_\odot$ for a $M_\star = 10^{11} M_\odot$ galaxy) includingaccurate collisional dynamics in the vicinity of nuclear supermassive blackholes.

MSTAR -- a fast parallelised algorithmically regularised integrator with minimum spanning tree coordinates