I was under the impression that per reg T, you can borrow 100% of the equity value of your stock. So if you own $10,000 worth of stock, you can borrow $10,000 against it (but you will get margin called if there's a decline, so don't do that).

You're right however, if you want to acquire more shares using margin, then your equity needs to be at least 50% of the stock value, i.e. with $10k you can purchase (up to) $20k worth of stock.

Shorthand: You can borrow 50%.

You can't put $10K into the account, buy $10K in shares, and borrow $10K in cash (leaving 0 net equity in the account).

Your scenario where you can borrow 100% of the value applies only if you apply that 100% to further shares (meaning you buy 2x as many shares and have a margin balance of 100% of your original equity but 50% of the shares' value).

That means you can buy $20K worth of stock using $10K of cash.

Interesting. I don't usually use margin since I live in a country without capital gains tax, but if I transfer $10k worth of shares and I want to use it as a line of credit, then I can at most take out $5k (in cash) before getting margin called?

Yes and no (mostly yes). The 50% level is the "initial margin" limit (hence the "yes" part) for initiating a loan.

There is a separate, lower limit called the "maintenance margin" limit, which is the equity percentage that you need to hold to avoid a margin call on a held position.

So, if you deposit $10K in shares, they appreciate to $12K, you borrow $6K and then the share price falls back to the original amount, you have $10K in shares, $4K in net equity (40%), but are probably not going to receive a margin call.

Or, if they are worth $10K, you borrow the limit of $5K and the share price falls by 1%, you won't get a margin call there either (on most securities).

What happens when you pay up the loan? Can the bank get your shares without you paying tax?

Otherwise its just a collateral.