  Let $f(x,y), g(x,y)$ denote either a pair of holomorphic function germs, or a
pair of monic polynomials in $x$ whose coefficients are Laurent series in $y$.
A relative polar arc is a Newton-Puiseux root, $x=\gamma(y)$, of the Jacobian
$J=f_yg_x-f_xg_y$. We define the tree-model, $T(f,g)$, for the pair, using the
contact orders of the Newton-Puiseux roots of $f$ and $g$. We then describe how
the $\gamma$'s climb, and where they leave, the tree. We shall also show by two
examples that the way the $\gamma$'s leave the tree is not an invariant of the
tree; this phenomenon is in sharp contrast to that in the one function case
where the tree completely determines how the polar roots split away. Our result
yield a factorisation of the Jacobian determinant.
