  We report preliminary measurements of the branching fractions of the decays
$\tau \to K\, n\pi^0\, \nu$ ($n = 0,1,2,3$) and $\tau \to \pi\, n\pi^0\, \nu$
($n = 3,4$), excluding the contributions that proceed through the decay of
intermediate $K^0$ and $\eta$ mesons. The measurements are based on a data
sample of 435 million $\tau$ pairs produced in $e^+e^-$ collisions at and near
the $\Upsilon(4S)$ peak and collected with the BaBar detector in 1999-2008. The
measured branching fractions are $B(\tau^- \to K^- \nu_\tau) = (7.174 \pm 0.033
\pm 0.213) \times 10^{-3}$, $B(\tau^- \to K^- \pi^0 \nu_\tau) = (5.054 \pm
0.021 \pm 0.148) \times 10^{-3}$, $B(\tau^- \to K^- 2\pi^0 \nu_\tau) = (6.151
\pm 0.117 \pm 0.338) \times 10^{-4}$, $B(\tau^- \to K^- 3\pi^0 \nu_\tau) =
(1.246 \pm 0.164 \pm 0.238) \times 10^{-4}$, $B(\tau^- \to \pi^- 3\pi^0
\nu_\tau) = (1.168 \pm 0.006 \pm 0.038) \times 10^{-2}$, $B(\tau^- \to \pi^-
4\pi^0 \nu_\tau) = (9.020 \pm 0.400 \pm 0.652) \times 10^{-4}$, where the first
uncertainty is statistical and the second one systematic.
