does it assume your forum name is the same as the BTS account you hold your funds on?
No. First it queries all the asset holders and builds a list, lets suppose you're looking up the asset "XASSET", and there's 3 people who hold this, we first build a quote, which looks like this:
[["persona", 100], ["personb", 200], ["personc", 150]]
where these are their bts accounts
not you're forum accounts.
Then lets say, we want to drop 1000 YASSET on these holders, the way we calculate this is determining the %-holding of each user. First we compute S the total sum of all the assets:
S = 100+200+150 = 450
So now we can determine the amount of YASSET they should get,
persona = 1000 YASSET * (100/450)
personb = 1000 YASSET * (200/450)
personc = 1000 YASSET * (140/450)
this is sent out as an
actual transaction (transfer2) meaning there
is a fee per each transaction (we estimate, or at least charge 45 BTS per tx).
When you share drop, via sharebits, you're sending funds
directly to the asset holders' BTS accounts.