  We introduce the theater model, which is the simplest variant of directed
random sequential adsorption in one dimension with point source and steric
interactions. Particles enter sequentially an initially empty row of $L$ sites
and adsorb irreversibly at randomly chosen places. If two particles occupy
adjacent sites, they prevent further particles from passing them. A jammed
configuration without available empty sites is eventually reached. More
generally, we investigate the class of models parametrized by $b$, the number
of consecutive particles needed to form a blockage. We show analytically that
the occupations of different sites in jammed configurations exhibit long-range
correlations obeying scaling laws, for all integers $b\ge2$, so that the total
number of particles grows as a subextensive power of $L$, with exponent
$(b-1)/b$, and keeps fluctuating even for very large systems. The exactly known
relative number variance measuring this lack of self-averaging is maximal for
the theater model {\it stricto sensu} ($b=2$). In the special case where $b=1$,
so that each adsorbed particle is a blockage, the model can be mapped onto the
statistics of records in sequences of random variables and of cycles in random
permutations. A two-sided variant of the model is also considered. In both
situations the number of particles grows only logarithmically with $L$, and it
is self-averaging.
