I'll quote myself from elsewhere:

Quote Originally Posted by Apoc
As to the titles & heirlooms: most of them get reassigned when their owner dies (provided the conditions are met). Lord of Westfold, for instance, is given to any captain (general) that spends a turn in Helm's Deep if there is no captain currently with that ancillary (simulating you granting them lordship). The same is true for all the other 'titles', i.e. they are tied to settlements. The Black Horn is given to any captain with the 'House of Erkenbrand' trait (which is a trait passed on from father to legitimate son), so the only way this will not be reassigned is if that House 'dies'. Most other heirlooms tied to faction leaders/heirs get regenerated with the new king/heir. You can also move ancillaries around manually, if your captains/spies/assassins/emissaries are in the same army/settlement; just open the character scroll, grab and draw the ancillary image over the image of the character you wish to give the ancillary to. This is a good way of giving younger captains a head start by giving them ancillaries from older (and soon to be dead) captains - and also what you want to be doing if you notice that the last of the House of Erkenbrand is son-less.
Quote Originally Posted by Apoc
To add to that: heirlooms/offices, such as Andúril or Lord of Emyn Arnen, always get passed on, though a few have certain conditions attached to them (Steward of Gondor will only be given to a captain from the House of Húrin, for example). Other items, such as Elven Sword or Dwarven Helm, are more difficult to get and should probably be passed on manually if you want to keep them.

If anyone has any questions regarding traits and ancillaries, I'll be happy to answer them here.

I have been wondering, though: Have anyone got a full set of Elven or Dwarven armour/weapons (helm/hauberk/sword)? Or the mithril armour set? What about the Haradrian Kathuphazgân trait?
I hope that answers some of your questions!