  In the kinematic region where three particles $i$, $j$, $k$ are collinear,
the multi-parton scattering amplitudes factorise into a product of a triple
collinear splitting function and a multi-parton scattering amplitude with two
fewer particles. These triple collinear splitting functions contain both
iterated single unresolved contributions, and genuine double unresolved
contributions. We make this explicit by rewriting the known triple collinear
splitting functions in terms of products of two-particle splitting functions,
and a remainder that is explicitly finite when any two of $\{i,j,k\}$ are
collinear. We analyse all of the single unresolved singularities present in the
remainder.
