  We study by computer simulation a recently introduced generalised model of
self-interacting self-avoiding trails on the square lattice that distinguishes
two topologically different types of self-interaction: namely crossings where
the trail passes across itself and collisions where the lattice path visits the
same site without crossing. This model generalises the canonical interacting
self-avoiding trail model of polymer collapse which has a strongly divergent
specific heat at its transition point. We confirm the recent prediction that
the asymmetry does not affect the universality class for a range of asymmetry.
Certainly, where the weighting of collisions outweighs that of crossings this
is well supported numerically. When crossings are weighted heavily relative to
collisions the collapse transition reverts to the canonical theta-point-like
behaviour found in interacting self-avoiding walks.
