  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 $\Lav$ is effectively
comparable to that of laboratory experiments (up to 5000 monomers, even at high
polymer densities). We sample up to scission energies of $E/k_BT=15$ 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 $\Lav \propto \phi^\alpha \exp(\delta
E)$ where the exponents approach $\alpha_d=\delta_d=1/(1+\gamma) \approx 0.46$
and $\alpha_s = 1/2 [1+(\gamma-1)/(\nu d -1)] \approx 0.6, \delta_s=1/2$ in the
dilute and semidilute limits respectively. The chain length distribution is
qualitatively well described in the dilute limit by the Schulz-Zimm
distribution $\cN(s)\approx s^{\gamma-1} \exp(-s)$ where the scaling variable
is $s=\gamma L/\Lav$. The very large size of these simulations allows also an
accurate determination of the self-avoiding walk susceptibility exponent
$\gamma \approx 1.165 \pm 0.01$. ....... Finite-size effects are discussed in
detail.
