  This work studies the jamming and percolation of parallel squares in a
single-cluster growth model. The Leath-Alexandrowicz method was used to grow a
cluster from an active seed site. The sites of a square lattice were occupied
by addition of the equal size $k \times k$ squares (E-problem) or a mixture of
$k \times k$ and $m \times m$ ($m \leqslant k$) squares (M-problem). The larger
$k \times k$ squares were assumed to be active (conductive) and the smaller $m
\times m$ squares were assumed to be blocked (non-conductive). For equal size
$k \times k$ squares (E-problem) the value of $p_j = 0.638 \pm 0.001$ was
obtained for the jamming concentration in the limit of $k\rightarrow\infty$.
This value was noticeably larger than that previously reported for a random
sequential adsorption model, $p_j = 0.564 \pm 0.002$. It was observed that the
value of percolation threshold $p_{\mathrm{c}}$ (i.e., the ratio of the area of
active $k \times k$ squares and the total area of $k \times k$ squares in the
percolation point) increased with an increase of $k$. For mixture of $k \times
k$ and $m \times m$ squares (M-problem), the value of $p_{\mathrm{c}}$
noticeably increased with an increase of $k$ at a fixed value of $m$ and
approached 1 at $k\geqslant 10m$. This reflects that percolation of larger
active squares in M-problem can be effectively suppressed in the presence of
smaller blocked squares.
