My brother and I want to open a joint brokerage account and invest 50/50. I was told the primary account holder is responsible for taxes. Do they do 100% of the capital gains taxes then give the secondary holder their profits? Or do they do 50% of the profits and the secondary holder does the other 50%? I wouldn't want the primary holder doing 100% of the taxes and then giving the secondary holder their profit only to see them get taxes on that money for a second time.

First any income you receive in cash should be split 50/50, and any income reinvested in the account should be considered jointly owned 50/50 as well. The primary account holder will be the one who receives the income tax forms reporting all the income to the account - Forms 1099-INT, 1099-DIV, 1099-B, etc. as appropriate for the type of account. The "official" way to handle the split of income is for him as primary account holder to issue his own 1099 forms to you, reporting half the income, and file copies with the IRS. On his tax return he reports the full amount as reported on the forms(s) he receives, and subtracts the amount he passed on to you indicating "nominee distribution." That way he is taxed on half the income. Meanwhile you report the other half of the income on your own return based on the 1099 forms he issued to you. Details are provided under "Nominee Distributions" on page 19 of IRS Pub 550:
http://www.irs.gov/pub/irs-pdf/p550.pdf

That's the official way. If you and your brother are on good terms an easier way may be for him to simply report the full amount as income on his own tax return, and you reimburse him for half the amount that this adds to his tax bill. Of course this may not be exactly fair if you and he are in different tax brackets, but it's a lot simpler.

I regret not answering sooner, but the email from the website stopped for some reason and just resumed today.

In any event, ebaines covers the subject rather well, so I have nothing to add.