  Double parton distributions (DPDs) receive a short-distance contribution from
a single parton splitting to yield the two observed partons. We investigate
this mechanism at next-to-leading order (NLO) in perturbation theory.
Technically, we compute the two-loop matching of both the position and momentum
space DPDs onto ordinary PDFs. This also yields the 1 -> 2 splitting functions
appearing in the evolution of momentum-space DPDs at NLO. We give results for
the unpolarised, colour-singlet DPDs in all partonic channels. These quantities
are required for calculations of double parton scattering at full NLO. We
discuss various kinematic limits of our results, and we verify that the 1 -> 2
splitting functions are consistent with the number and momentum sum rules for
DPDs.
