Are you asking about gift tax or income tax? No income tax has to be paid until the stock is sold. There is no income tax at the time of the gift if the stock is transferred in kind. When the stock is sold, whoever owns it at that time and sells it has to report the sale on his or her income tax return and pay income tax on any gain.
Calculating the gain on stock that was received as a gift can get complicated. The recipient of the gift will need to know the date that the giver acquired the stock and how the giver acquired it. If the giver purchased the stock, the recipient will need to know how much the giver paid for it. If the giver acquired it by gift, inheritance, or in some other way, additional information will be needed. The recipient also needs to know the market value on the date of the gift, and how much gift tax the giver paid, if any.
If the stock pays dividends, whoever receives the dividends has to pay income tax on the dividends in the year that the dividends are paid.
