  Numerical simulations by means of Monte Carlo method and finite-size scaling
analysis have been performed to study the percolation behavior of linear
$k$-mers (also denoted in the literature as rigid rods, needles, sticks) on
two-dimensional square lattices $L \times L$ with periodic boundary conditions.
Percolation phenomena are investigated for anisotropic relaxation random
sequential adsorption of linear $k$-mers. Especially, effect of anisotropic
placement of the objects on the percolation threshold has been investigated.
Moreover, the behavior of percolation probability $R_L(p)$ that a lattice of
size $L$ percolates at concentration $p$ has been studied in details in
dependence on $k$, anisotropy and lattice size $L$. A nonmonotonic size
dependence for the percolation threshold has been confirmed in isotropic case.
We propose a fitting formula for percolation threshold $p_c =
a/k^{\alpha}+b\log_{10} k+ c$, where $a$, $b$, $c$, $\alpha$ are the fitting
parameters varying with anisotropy. We predict that for large $k$-mers
($k\gtrapprox 1.2\times10^4$) isotropic placed at the lattice, percolation
cannot occur even at jamming concentration.
