Nobody pays tax on the gain that accrued prior to your grandmother's death. That's the great benefit of "stepped up basis." The basis of the stock is the fair market value on the date of her death. Only the gain after that date is taxable. The gain that accrued prior to her death disappears and is never taxed. And it doesn't matter whether the estate sells the stock or the beneficiaries sell the stock. Either the estate or the beneficiaries get the stepped up basis.
If you distribute the shares to the beneficiaries, for the purpose of calculating taxable gain, "the day they took ownership" is the date of your grandmother's death, even though title is not actually transferred until later.
You don't "pay capital gains." Capital gain is the profit you make from selling a stock or other investment. The capital gain is income that you receive, not something that you pay. You pay income tax on the capital gain income that you received.
