Annual Gift Exclusion = $14,000 right now, and this increases every few years.
If the amount given to your father exceeds that, you should re-think the strategy a bit. If it's less than that, no one will be required to pay any taxes on these gifts/transfers. After the gifts are made and you hold the asset, you are then responsible for any income it produces.
If Gramps is giving > $14,000 to your dad you still might be ok. Is there a mom/wife in the mix here? If so, gramps can give them each $14,000/year. In addition, he can give each of his grandchildren $14,000/year. If the grandchildren are married he can give their spouses $14,000/year as well.
If gramps is giving > any of the amounts described above, gramps should be filing annual gift tax returns and claiming these gifts. He will likely not have to pay any taxes on the gifts, they will simply reduce his lifetime exclusion (The $5M number). Only when he gives > the lifetime exclusion will anyone have to pay any taxes on the transfer if you do it properly.