Final answer:
Upon the sister's death, the nephew, being the designated remainderman, automatically becomes the fee simple owner of the property, as was originally arranged when the life estate was established.
Step-by-step explanation:
If a property owner conveys a life estate to his sister for her lifetime and then designates his nephew as the person to whom the property will pass when the life estate ends, the outcome upon the sister's death is as follows.
Since his nephew has been designated beforehand, he is considered the remainderman of the property.
As per the arrangement of a life estate with a named remainderman, upon the sister's death, the property does not revert back to the original property owner, nor does it pass to the sister's heirs. Instead, the nephew automatically becomes the fee simple owner of the property.