  We show that the honeycomb Heisenberg antiferromagnet with $J_1/2=J_2=J_3$,
where $J_{1/2/3}$ are first-, second- and third-neighbour couplings
respectively, forms a classical spin liquid with pinch-point singularities in
the structure factor at the Brillouin zone corners. Upon dilution with
non-magnetic ions, fractionalised degrees of freedom carrying $1/3$ of the free
moment emerge. Their effective description in the limit of low-temperature is
that of spins randomly located on a triangular lattice, with a frustrated
interaction of long-ranged logarithmic form. The XY version of this magnet
exhibits nematic thermal order by disorder, which comes with a clear
experimental diagnostic.
