How do underway interceptions work on the campaign map?

[SpiffyGonzales]

So I always figured that if i didnt pass the enemy armies ZOC than i wouldnt get it, turn 300 as BM in mortal empires, but a couple times against dwarfs they intercept even without me going in the direction of their Zone of Control.
Is it irrelevant to the interception?
do interceptions just happen without armies?
do THEY just happen to have armies in the underway i dont see?

I'm just curious how the whole shabang works is all : )

[NO PASARÁN 161]

I think underway/beastpath interceptions can happen when crossing an enemy army's movement range.

[sixela1]

Interception range is 10 tiles. Army ZOC range is 3.5 tiles i think