Does nightfall's additional weapon damage apply to the primary target as well?

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Short answer is yes.

It’s like a separate proc though so it’s not additive in terms of lets say stacking %dmg for dots. Unaffected by direct SS mods or ndje % crit just the CDR of course

If it’s a separate proc, would it apply 40% of any flat DoT you have?

To mobs in it’s AoE yes, to main Target SS much higher %wp damage would take the lead and overwrite.

But Abb at 1 pt + skills would overwrite NB in AoE as well.