  In this paper we consider a connected planar graph $G$ and impose conditions
that results in $G$ having a percolation lattice-like cellular structure.
Assigning each cell of $G$ to be either occupied or vacant, we describe the
outermost boundaries of star and plus connected components in $G$. We then
consider the dual graph of $G$ and impose conditions under which the dual is
also a percolation lattice. Finally, using $G$ and its dual, we construct
vacant cell cycles surrounding occupied components and study left right
crossings and bond percolation in rectangles.
