  We perform a Monte Carlo simulation of two-dimensional N-step interacting
self-avoiding walks at the theta point, with lengths up to N=3200. We compute
the critical exponents, verifying the Coulomb-gas predictions, the theta-point
temperature T_theta = 1.4986(11), and several invariant size ratios. Then, we
focus on the geometrical features of the walks, computing the instantaneous
shape ratios, the average asphericity, and the end-to-end distribution
function. For the latter quantity, we verify in detail the theoretical
predictions for its small- and large-distance behavior.
