  We study analytically and numerically a model of random sequential adsorption
(RSA) of segments on a line, subject to some constraints suggested by two kinds
of physical situations:
  - deposition of dimers on a lattice where the sites have a spatial extension;
  - deposition of extended particles which must overlap one (or several)
adsorbing sites on the substrate.
  Both systems involve discrete and continuous degrees of freedom, and, in one
dimension, are equivalent to our model, which depends on one length parameter.
When this parameter is varied, the model interpolates between a variety of
known situations : monomers on a lattice, "car-parking" problem, dimers on a
lattice. An analysis of the long-time behaviour of the coverage as a function
of the parameter exhibits an anomalous 1/t^2 approach to the jamming limit at
the transition point between the fast exponential kinetics, characteristic of
the lattice model, and the 1/t law of the continuous one.
