We present a systematic study of the extraplanar gas (EPG) in a sample of 15 nearby late-type galaxies at intermediate inclinations using publicly available, deep interferometric HI data from the HALOGAS survey. For each system we mask the HI emission coming from the regularly rotating disc and use synthetic datacubes to model the leftover anomalous HI flux. Our model consists of a smooth, axisymmetric thick component described by 3 structural and 4 kinematical parameters, which are fit to the data via a Bayesian MCMC approach. We find that extraplanar HI is nearly ubiquitous in disc galaxies, as we fail to detect it in only two of the systems with the poorest spatial resolution. The EPG component encloses ~5-25% of the total HI mass, with a mean value of 14%, and has a typical thickness of a few kpc, incompatible with expectations based on hydrostatic equilibrium models. The EPG kinematics is remarkably similar throughout the sample, and consists of a lagging rotation with typical vertical gradients of about -10 km/s/kpc, a velocity dispersion of 15-30 km/s and, for most galaxies, a global inflow in both the vertical and radial directions with speeds of 20-30 km/s. The EPG HI masses are in excellent agreement with predictions from simple models of the galactic fountain powered by stellar feedback. The combined effect of photo-ionisation and interaction of the fountain material with the circumgalactic medium can qualitatively explain the kinematics of the EPG, but dynamical models of the galactic fountain are required to fully test this framework.
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