  We study the function $M(n,k)$ which denotes the number of maximal
$k$-uniform intersecting families $F\subseteq \binom{[n]}{k}$. Improving a
bound of Balogh at al. on $M(n,k)$, we determine the order of magnitude of
$\log M(n,k)$ by proving that for any fixed $k$, $M(n,k)
=n^{\Theta(\binom{2k}{k})}$ holds. Our proof is based on Tuza's set pair
approach.
  The main idea is to bound the size of the largest possible point set of a
cross-intersecting system. We also introduce and investigate some related
functions and parameters.
