  The system-size dependence of hadrochemistry at vanishing baryon density is
considered within the canonical statistical model (CSM) with local exact
conservation of three conserved charges, allowing for a possibility of
strangeness undersaturation, i.e. $\gamma_S \leq 1$. Exact baryon number
conservation is found to be even more important than that of strangeness in the
canonical suppression picture at the LHC, in contrast to intermediate and low
collision energies. The model is applied to p-p, p-Pb, and Pb-Pb data of the
ALICE collaboration. A chemical equilibrium CSM with a fixed $T_{\rm ch} = 155$
MeV describes the trends seen in most yield ratios. However, this vanilla
version of CSM predicts an enhancement of the $\phi/\pi$ ratio at smaller
multiplicities, in stark contrast to the suppression seen in the data. The data
are described with a 15% relative accuracy level whence a multiplicity
dependence of both the temperature and the strangeness saturation parameter
$\gamma_S \leq 1$ is accepted. Both the canonical suppression and the
strangeness undersaturation effects are small at $d N_{\rm ch} / d\eta \gtrsim
100$, but they do improve substantially the description of hadron yields in p-p
collisions, in particular the $\Omega$ yields. A possibility to constrain the
rapidity correlation volume using net-proton fluctuation measurements is
pointed out.
