  We study numerically the effect of sequence heterogeneity on the
thermodynamic properties of a Poland-Scheraga model for DNA denaturation taking
into account self-avoidance, i.e. with exponent c_p=2.15 for the loop length
probability distribution. In complement to previous on-lattice Monte Carlo like
studies, we consider here off-lattice numerical calculations for large sequence
lengths, relying on efficient algorithmic methods. We investigate finite size
effects with the definition of an appropriate intrinsic length scale x,
depending on the parameters of the model. Based on the occurrence of large
enough rare regions, for a given sequence length N, this study provides a
qualitative picture for the finite size behavior, suggesting that the effect of
disorder could be sensed only with sequence lengths diverging exponentially
with x. We further look in detail at average quantities for the particular case
x=1.3, ensuring through this parameter choice the correspondence between the
off-lattice and the on-lattice studies. Taken together, the various results can
be cast in a coherent picture with a crossover between a nearly pure system
like behavior for small sizes N < 1000, as observed in the on-lattice
simulations, and the apparent asymptotic behavior indicative of disorder
relevance, with an (average) correlation length exponent \nu_r >= 2/d (=2).
