the walk (a function of $a$)
  $R_n^2$                    The mean square radius of gyration of the walk (a function of $a$)
  $P^+(\eps)$                The microcanonical density function (see equation )
  $a_c^+$                    The adsorption critical point
  $\phi$                     The crossover exponent
  $\alpha$                   The specific heat exponent
  $\gamma_1$                 The half-space entropic exponent, see also $\gamma_s$ (the surface exponent)
  $\nu$                      The metric exponent
  $G(a,t)$                   Generating function of $Z_n(a)$ (see equation )
  $G_N(a,t)$                 Truncated generating function (see equation )
  $t_c^+(a)$                 The radius of convergence of $G(a,t)$

  : Short list of definitions[]{data-label="Defs"}

Organisation of the manuscript
------------------------------

This paper is a report on two aspects of the Monte Carlo simulation of adsorbing walks. The first is the generalisation of the GAS algorithm to a model of interacting walks, and in particular, an implementation of this algorithm to achieve flat histogram sampling over state space of adsorbing square and cubic lattice walks. The second aspect of the paper is a report on the properties of adsorbing self-avoiding walks in the square and cubic lattices. The aim here is to verify the results obtained in the Multiple Markov Chain Monte Carlo study in reference [@JvRR04], and also to use the data generated here to test the scaling of the thermodynamic 