  Consider random sequential adsorption on a chequerboard lattice with arrivals
at rate $1$ on light squares and at rate $\lambda$ on dark squares. Ultimately,
each square is either occupied, or blocked by an occupied neighbour. Colour the
occupied dark squares and blocked light sites {\em black}, and the remaining
squares {\em white}. Independently at each meeting-point of four squares, allow
diagonal connections between black squares with probability $p$; otherwise
allow diagonal connections between white squares. We show that there is a
critical surface of pairs $(\lambda, p)$, containing the pair $(1,0.5)$, such
that for $(\lambda, p)$ lying above (respectively, below) the critical surface
the black (resp. white) phase percolates, and on the critical surface neither
phase percolates.
