  We employ relations between spacelike and timelike deep-inelastic processes
in perturbative QCD to calculate the next-to-next-to-leading order (NNLO)
contributions to the timelike quark-quark and gluon-gluon splitting functions
for the evolution of flavour-singlet fragmentation distributions. We briefly
address the end-point behaviour and the numerical size of these third-order
corrections, and write down the second moments of all four timelike splitting
functions. In the same manner we re-derive the NNLO result for the Higgs-boson
decay rate into hadrons in the limit of a heavy top quark and five massless
flavours, and confirm the recent N^3LO computation of this quantity.
