The nine-year H.E.S.S. Galactic Plane Survey (HGPS) yielded the most uniform observation scan of the inner Milky Way in the TeV gamma-ray band to date. The sky maps and source catalogue of the HGPS allow for a systematic study of the population of TeV pulsar wind nebulae found throughout the last decade. To investigate the nature and evolution of pulsar wind nebulae, for the first time we also present several upper limits for regions around pulsars without a detected TeV wind nebula. Our data exhibit a correlation of TeV surface brightness with pulsar spin-down power $dot{E}$. This seems to be caused both by an increase of extension with decreasing $dot{E}$, and hence with time, compatible with a power law $R_mathrm{PWN}(dot{E}) sim dot{E}^{-0.65 pm 0.20}$, and by a mild decrease of TeV gamma-ray luminosity with decreasing $dot{E}$, compatible with $L_{1-10,mathrm{TeV}} sim dot{E}^{0.59 pm 0.21}$. We also find that the offsets of pulsars with respect to the wind nebula centres with ages around 10 kyr are frequently larger than can be plausibly explained by pulsar proper motion and could be due to an asymmetric environment. In the present data, it seems that a large pulsar offset is correlated with a high apparent TeV efficiency $L_{1-10,mathrm{TeV}}/dot{E}$. In addition to 14 HGPS sources considered as firmly identified pulsar wind nebulae and 5 additional pulsar wind nebulae taken from literature, we find 10 HGPS sources that form likely TeV pulsar wind nebula candidates. Using a model that subsumes the present common understanding of the very high-energy radiative evolution of pulsar wind nebulae, we find that the trends and variations of the TeV observables and limits can be reproduced to a good level, drawing a consistent picture of present-day TeV data and theory.
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