  We use the latest all-sky continuous gravitational-wave (CW) searches to
estimate constraints on the sub-kiloparsec population of unknown neutron stars
(NS). We then extend this analysis to the forthcoming LIGO-Virgo-KAGRA
observing runs and the third generation (3G) of ground-based interferometric
detectors (Einstein Telescope and Cosmic Explorer). We find that sources with
ellipticities greater than $\epsilon \gtrsim 10^{-7}$ can be well-constrained
by current and future detectors regardless of their frequency. 3G detectors
will extend these constraints down to $\epsilon \gtrsim 10^{-8}$ across the
whole sensitive band and $\epsilon \gtrsim 10^{-9}$ above $1\,\textrm{kHz}$. We
do not expect $\epsilon \lesssim 10^{-8}$ sources to be constrained below
$1\,\textrm{kHz}$. Finally, we discuss the potential impact of using
astronomical priors on all-sky searches in terms of sensitivity and computing
cost. The populations here described can be used as a guide to set up future
all-sky CW searches.
