  In the limit where partons become collinear to each other, scattering
amplitudes factorize into a product of universal, process-independent building
blocks and scattering amplitudes involving fewer partons. We compute these
universal building blocks -- known as splitting amplitudes -- for two collinear
QCD partons up to third loop order in QCD. Our results describe arbitrary
time-like splitting processes. Due to the violation of strict collinear
factorization in space-like splitting processes, we specifically present
space-like splitting amplitudes for three-parton QCD scattering amplitudes at
third loop order. To achieve our results, we perform a collinear expansion of
three-loop scattering amplitudes using a new expansion-by-subgraph technology,
which is based on the method of regions.
