  We investigate the presence of hub-filament systems in a large sample of 146
active proto-clusters, using H$^{13}$CO$^{+}$ J=1-0 molecular line data
obtained from the ATOMS survey. We find that filaments are ubiquitous in
proto-clusters, and hub-filament systems are very common from dense core scales
($\sim$0.1 pc) to clump/cloud scales ($\sim$1-10 pc). The proportion of
proto-clusters containing hub-filament systems decreases with increasing dust
temperature ($T_d$) and luminosity-to-mass ratios ($L/M$) of clumps, indicating
that stellar feedback from H{\sc ii} regions gradually destroys the
hub-filament systems as proto-clusters evolve. Clear velocity gradients are
seen along the longest filaments with a mean velocity gradient of 8.71 km
s$^{-1}$pc$^{-1}$ and a median velocity gradient of 5.54 km s$^{-1}$pc$^{-1}$.
We find that velocity gradients are small for filament lengths larger than
$\sim$1~pc, probably hinting at the existence of inertial inflows, although we
cannot determine whether the latter are driven by large-scale turbulence or
large-scale gravitational contraction. In contrast, velocity gradients below
$\sim$1~pc dramatically increase as filament lengths decrease, indicating that
the gravity of the hubs or cores starts to dominate gas infall at small scales.
We suggest that self-similar hub-filament systems and filamentary accretion at
all scales may play a key role in high-mass star formation.
