ToME: the Tales of Maj'Eyal

How are weapon damage multipliers applied to on-hit damage from weapons?

Lets say I have a vanilla offhand dagger and I do 50% damage with my offhand, per skills. It is easy to intuit that I hit for 50% of the total damage of the weapon.

Change that to a dagger that does 10 fire damage on hit. Do I then hit for 50% of the regular damage + 50% of the fire damage? or 50% of the weapon damage and 100% of the fire damage?

+10 on-hit fire is simply +10 on-hit fire. It is not multiplied by anything except fire damage increasers (e.g. ring of fire that gives +12% to all fire damage). Talents only multiply the actual weapon damage, not the on-hit elemental bonuses.

In case this isn't obvious, it means that for everyone except those with really high two-weapon combat skill, you want a weapon with high on-hit damage effects in your off-hand; similarly, if you're using a low level of Flurry or other skills that reduce weapon damage, on-hit effects become much more important, while when using high damage multipliers (or a build that does lots of crits), actual weapon damage becomes more important.