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For a model of DNA denaturation [1], exponents describing the distributions of denaturated loops and unzipped end segments are determined by exact enumeration and by Monte Carlo simulations in two and three dimensions. The loop distributions are consistent with first-order thermal denaturation in both cases. Results for end segments show a coexistence of two distinct power laws in the relative distributions, which is not foreseen by a recent approach in which DNA is treated as a homogeneous network of linear polymer segments. This unexpected feature, and the discrepancies with such an approach, are explained in terms of a refined scaling picture in which a precise distinction is made between network branches representing single-stranded and effective double-stranded segments. The linking number (topological entanglement) of a similar model of circular double stranded DNA undergoing a denaturation transition is investigated [2]. By allowing the linking number to fluctuate freely in equilibrium we see that the linking probability undergoes an abrupt variation (first-order) at the denaturation transition, and stays close to 1 in the whole native phase. The average linking number is almost zero in the denatured phase and grows as the square root of the chain length, N, in the native phase. © 2003 American Institute of Physics [ABSTRACT FROM AUTHOR]