We report results of extensive dynamical Monte Carlo investigations on self-assembled equilibrium polymers (EP) without loops in good solvent. (This is thought to provide a good model of giant surfactant micelles.) Using a novel algorithm we are able to describe efficiently both static and dynamic properties of systems in which the mean chain length [L] is effectively comparable to that of laboratory experiments (up to 5000 monomers, even at high polymer densities). We sample up to scission energies of E/k(B)T= 15 over nearly three orders of magnitude in monomer density phi, and present a detailed crossover study ranging from swollen EP chains in the dilute regime up to dense molten systems. Confirming recent theoretical predictions, the mean-chain length is found to scale as [L]proportional to phi(alpha)exp(delta E) where the exponents approach alpha(d) = delta(d) = 1/(1 + gamma) approximate to 0.46 and alpha(s) = 1/2[1 + (gamma - 1)/(vd - 1)] approximate to 0.6, delta(s) = 1/2 in the dilute and semidilute limits respectively. The chain length distribution is qualitatively well described in the dilute limit by the Schulz-Zimm distribution p(s) approximate to s(gamma-1) exp(-s) where the scaling variable is s = gamma L/[L]. The very large size of these simulations allows also an accurate determination of the self-avoiding walk susceptibility exponent y approximate to 1.165 +/- 0.01. As chains overlap they enter the semidilute regime where the distribution becomes a pure exponential p(s) = exp( -s) with the scaling variable now s = LI(L). In addition to the above results we measure the specific heat per monomer c(v). We show that the average size of the micelles, as measured by the end-to-end distance and the radius of gyration, follows a crossover scaling that is, within numerical accuracy, identical to that of conventional monodisperse quenched polymers. Finite-size effects are discussed in detail. (C) 1998 American Institute of Physics.