  Continuum Schwinger function methods for the strong-interaction bound-state
problem are used to arrive at a unified set of parameter-free predictions for
the semileptonic $K\to \pi$, $D\to \pi, K$ and $D_s \to K$, $B_{(s)} \to
\pi(K)$ transition form factors and the associated branching fractions. The
form factors are a leading source of uncertainty in all such calculations: our
results agree quantitatively with available data and provide benchmarks for the
hitherto unmeasured $D_s\to K^0$, $\bar B_s \to K^+$ form factors. The analysis
delivers a value of $|V_{cs}| = 0.974(10)$ and also predictions for all
branching fraction ratios in the pseudoscalar meson sector that can be used to
test lepton flavour universality. Quantitative comparisons are provided between
extant theory and the recent measurement of ${\cal B}_{B_s^0\to K^- \mu^+
\nu_\mu}$. Here, further, refined measurements would be useful in moving toward
a more accurate value of $|V_{ub}|$.
