I still cannot find the patter nhow the merchant take overs works...

[Handel]

Just an example - recently my 5 stars merchant ON MY OWN LANDS (France) had only 48% chance against an enemy 3 stars merchant. I don't know what the logic is. The logical chance is 5/3 or 62,5% and as even without any "home" bonuses.
BTW - there are definetely some "home" bonuses because I attacked a merchant outside my borders and I needed 2 turns for it; but the next turn the enemy merchant entered my territory and the chances increased with about 15%.

[FactionHeir]

As I will not be touching the game till friday I can't tell you exact test results, but to find it out yourself, do the following:

Find any hostile merchant. Find a nearby own merchant. Now try the various finance level comparisons against the foreign one by doing following:

i.e. he has 3 finance.
You can now use:
give_trait this GoodMerchant (0-4)
give_trait this Monopolist (0-3)
give_trait this WorldlyMerchant (0-2)
give_trait this NaturalMerchantSkill (0-3)

without the brackets.
This will allow you to modify how much skill your own merchant has while he is selected. Now try to find a progression between skill levels against the enemy merchant, it should be fairly easy.

Afaik, there is no home bonus, chances are your merchant got one of the silent merchant traits when you ended the turn. (legal line, worldly merchant line, monopolist line)