  The two-dimensional dense O(n) loop model for $n=1$ is equivalent to the bond
percolation and for $n=0$ to the dense polymers or spanning trees. We consider
the boundary correlations on the half space and calculate the probability $P_b$
that a cluster of bonds has a single common point with the boundary. In the
limit $n\rightarrow 0$, we find an analytical expression for $P_b$ using the
generalized Kirchhoff theorem.
