  We study a relation recently derived by K. Kondo at zero momentum between the
Zwanziger's horizon function, the ghost dressing function and Kugo's functions
$u$ and $w$. We agree with this result as far as bare quantities are
considered. However, assuming the validity of the horizon gap equation, we
argue that the solution $w(0)=0$ is not acceptable since it would lead to a
vanishing renormalised ghost dressing function. On the contrary, when the
cut-off goes to infinity, $u(0) \to \infty$, $w(0) \to -\infty$ such that
$u(0)+w(0) \to -1$. Furthermore $w$ and $u$ are not multiplicatively
renormalisable. Relaxing the gap equation allows $w(0)=0$ with $u(0) \to -1$.
In both cases the bare ghost dressing function, $F(0,\Lambda)$, goes
logarithmically to infinity at infinite cut-off. We show that, although the
lattice results provide bare results not so different from the $F(0,\Lambda)=3$
solution, this is an accident due to the fact that the lattice cut-offs lie in
the range 1-3 GeV$^{-1}$. We show that the renormalised ghost dressing function
should be finite and non-zero at zero momentum and can be reliably estimated on
the lattice up to powers of the lattice spacing ; from published data on a
$80^4$ lattice at $\beta=5.7$ we obtain $F_R(0,\mu=1.5$ GeV)$\simeq 2.2$.
