  Let $\epsilon >0$. A continuous linear operator
  $T:C(X) \ra C(Y)$ is said to be {\em $\epsilon$-disjointness preserving} if
$\vc (Tf)(Tg)\vd_{\infty} \le \epsilon$, whenever $f,g\in C(X)$ satisfy $\vc
f\vd_{\infty} =\vc g\vd_{\infty} =1$ and $fg\equiv 0$. In this paper we address
basically two main questions:
  1.- How close there must be a weighted composition operator to a given
$\epsilon$-disjointness preserving operator?
  2.- How far can the set of weighted composition operators be from a given
$\epsilon$-disjointness preserving operator?
  We address these two questions distinguishing among three cases: $X$
infinite, $X$ finite, and $Y$ a singleton ($\epsilon$-disjointness preserving
functionals).
  We provide sharp stability and instability bounds for the three cases.
