Legal issue: do you own the stocks now free and clear or do you have to go through probate?
Answer: I don't know, it will depend on how the account was titled and the laws of your state. A joint account may be different than a survivors account. I assume you will be getting legal advice on other estate matters (selling a house, etc.). Ask the attorney this question too.
Tax question: What's taxable?
Answer: If you inherited the stocks, then your cost basis is the value on the day he died. The proceeds from a sale would be taxable to the extent you have a capital gain (sell for more than the price on the day he died.) However, if you were made a co-owner by gift when the account was placed in your name, things become much more complicated. "Right of survivorship" usually means that you inherited the stocks at their full value on the day he died, but this again might be worth having reviewed.
