HoM dedications question

When you dedicate something to the HoM do you lose it from your inventory or is it just considered dedicated for the purposes of tracking things you have achieved?

A weapon is customized for use only by that character or that character's heroes.

A minipet is "dedicated" which means it can only be added to a single account's HoM. It is not customized, and can still be traded and used by other characters on your account or anyone else's.

Armor is just added, nothing changes, the same is true with heroes and animal companions.

So it sounds like I can dedicate the things I've gotten from the anniversary presents to the HoM but still be able to use them after I do.

That is correct.

Yup, and if you dedicate a weapon, it will become "customized" for the character who dedicated it, just like you would do at a weaponsmith. The 20% bonus is included, just like the weaponsmith.

Shields and offhands get customized in this fashion, which is something you CAN'T do at a weaponsmith. (no extra 20% bonus for this though, lol, wouldn't that be sweet?)