  Jamming and percolation of square objects of size $k \times k$ ($k^2$-mers)
isotropically deposited on simple cubic lattices have been studied by numerical
simulations complemented with finite-size scaling theory. The $k^2$-mers were
irreversibly deposited into the lattice. Jamming coverage $\theta_{j,k}$ was
determined for a wide range of $k$ ($2 \leq k \leq 200$). $\theta_{j,k}$
exhibits a decreasing behavior with increasing $k$, being
$\theta_{j,k\rightarrow\infty}=0.4285(6)$ the limit value for large $k^2$-mer
sizes. On the other hand, the obtained results shows that percolation
threshold, $\theta_{c,k}$, has a strong dependence on $k$. It is a decreasing
function in the range $2 \leq k \leq 18$ with a minimum around $k=18$ and, for
$k \geq 18$, it increases smoothly towards a saturation value. Finally, a
complete analysis of critical exponents and universality has been done, showing
that the percolation phase transition involved in the system has the same
universality class as the 3D random percolation, regardless of the size $k$
considered.
