The cost basis in a gift or inheritance is not zero. For a gift, your cost basis is the giver's basis (usually what he paid for it). For an inherited item, the cost basis is the fair market value on the date of death.
For an appreciated asset (usually stocks or mutual funds), you may deduct the current value (rather than just your cost basis), but only if the asset is "long term" (held one year or more). All inherited items are considered long term. For a gift, the giver's holding period transfers to you. For example, if Mom gives you a stock she has had for years, it is long term to you, even if you sell it (or donate it) the same day you receive it.
