  Given two independent Poisson point processes $\Phi^{(1)},\Phi^{(2)}$ in
$R^d$, the continuum AB percolation model is the graph with points of
$\Phi^{(1)}$ as vertices and with edges between any pair of points for which
the intersection of balls of radius $2r$ centred at these points contains at
least one point of $\Phi^{(2)}$. This is a generalization of the $AB$
percolation model on discrete lattices. We show the existence of percolation
for all $d > 1$ and derive bounds for a critical intensity. We also provide a
characterization for this critical intensity when $d = 2$. To study the
connectivity problem, we consider independent Poisson point processes of
intensities $n$ and $cn$ in the unit cube. The $AB$ random geometric graph is
defined as above but with balls of radius $r$. We derive a weak law result for
the largest nearest neighbour distance and almost sure asymptotic bounds for
the connectivity threshold.
