  Random sequential adsorption of linear and square particles with excluded
volume interaction is studied numerically on planar lattices considering
Gaussian distributions of lateral sizes of the incident particles, with several
values of the average and of the width-to-average ratio $w$. When the coverage
is plotted as function of the logarithm of time $t$, the maximum slope is
attained at a time $t_M$ of the same order of the time $\tau$ of incidence of
one monolayer, which is related to the molecular flux and/or sticking
coefficients. For various values of the average $\mu$ and $w$, we obtain
$1.5\tau < t_M < 5\tau$ for linear particles and $.3\tau< t_M < \tau$ for
square particles. At $t_M$, the coverages with linear and square particles are
near .3 and .2, respectively. Extrapolations show that coverages may vary with
$\mu$ up to 20% and 2% for linear and square particles, respectively, for
$\mu\ge 64$, fixed time, and constant $w$. All coverage $\theta$ versus $\log
t$ plots have approximately the same shape, but other quantities measured at
times of order $t_M$ help to distinguish narrow and broad incident
distributions. The adsorbed particle size distributions are close to the
incident ones up to long times for small $w$, but appreciably change in time
for larger $w$, acquiring a monotonically decreasing shape for $w = 1/2$ at
times of order $100\tau$ . At $t_M$, incident and adsorbed distributions are
approximately the same for $w \le 1/8$ and show significant differences for $w
\ge 1/2$; this result may be used as a consistency test in applications of the
model. The pair correlation function $g (r; t)$ for $w = 1/8$ has a well
defined oscillatory structure at $10t_M$, with a minimum at $r\approx\mu$ and
maximum at $r \approx 1.5\mu$, but this structure is not observed for $w \ge
1/4$.
