  Random sequential adsorption (RSA) is a standard method of modeling
adsorption of large molecules at the liquid-solid interface. Several studies
have recently conjectured that in the RSA of rectangular needles, or $k$-mers,
on a square lattice the percolation is impossible if the needles are
sufficiently long ($k$ of order of several thousand). We refute these claims
and present a strict proof that in any jammed configuration of nonoverlapping,
fixed-length, horizontal or vertical needles on a square lattice, all clusters
are percolating clusters.
