I haven’t asked any game officials about this but when I transferred Borim and Darpheren to Arkenstone 10 years ago, they left behind a lot of bound (to character) items that were in either my house, the kin house or shared storage. I don’t know what will happen with items that are bound to account.

Carvith and I went through most of the houses in our neighborhood and Returned to Owner any bound items.

I’ve gone through my SHARED STORAGE and moved all bound items to the personal vaults of the characters to whom they are bound.

I’ve gone through my HOUSE and moved all bound items to the personal vaults of the characters to whom they are bound.

Make sure your house storage isn’t overflowing. All the items Car and I Returned were sent there.

Unbound items will transfer with your characters. I believe your house items (escrow) will go with the character who purchased the house.