No, do not add your name. To avoid tax and legal problems, either buy them out or wait for the actual inheritance. On the other hand, if you have paid the mortgage for the last 20 years, you should have a written agreement for being repaid.
In my opinion, do not add your name to the deed of your parents house. It all has to do with capital gains tax. By adding your name, when it comes time to sell the house, your bases for tax goes all the way back to when your parents had bought the house. Depending on the market value of the house, you could find yourself paying high capital gains tax.
If you inherit the house via a Will, then the bases for capital gains would be what the house is worth on the day your had inherited the house.
Another issue would be if your parent or both need Medicaid. If they apply for Medicaid [to help them pay for a nursing home], if Medicaid sees that your parents had put your name on the Deed within the 5 year financial look back, then the equity that would be yours would be considered a "gift" thus subtracted from amount that Medicaid would be giving your parents for care.
To find out what would be best, contact an Elder Law Attorney.
If you inherit the house via a Will, then the bases for capital gains would be what the house is worth on the day your had inherited the house.
Another issue would be if your parent or both need Medicaid. If they apply for Medicaid [to help them pay for a nursing home], if Medicaid sees that your parents had put your name on the Deed within the 5 year financial look back, then the equity that would be yours would be considered a "gift" thus subtracted from amount that Medicaid would be giving your parents for care.
To find out what would be best, contact an Elder Law Attorney.