Answer: There is no distinctive Objectivist view on inheritance. Objectivism advocates laissez-faire, a free market economy in which all private trades between consenting adults (that do not violate the rights of another) are legal. It follows that any gifts one would care to give in one's lifetime would be legal. Inheritance, or the ability to leave bequests, is just the limiting case of gift-giving. Objectivism naturally opposes any extraordinary taxation of gifts, and this would in the limit imply opposing most estate taxes. Certainly, in the Objectivist view the state is not entitled to a person's wealth upon their decease. Nor does the wealth belong to "society." The wealth belonged to the deceased, and it was up to the deceased, while alive, to determine its disposition.
Now rights, in the Objectivist view, are principles that apply to us as living beings: the dead as such have no rights. Thus there may be an opening for a theorist working on Objectivist premises to offer some argument against trusts and other instruments by which the dead might exert their will into the future. But Objectivism
as such has no position on the matter, and its default view would be that establishing trusts is within the purview of the property owner. Again, it is hard to see why, given that one should be entitled to establish trusts to serve one's purposes while alive, that one should not be able to establish them as one's final living act.
A regime of untaxed bequests sounds likely to create an aristocracy of plutocrats who pass wealth from one generation to the next. But this is an illusion. I researched this matter while in graduate school. Intergenerational correlations of wealth are not very high, and were not high even under the more laissez-faire policies of the early 20th-century. Basically, in most families the wealth earned by the grandparents is entirely dissipated by the time the grandchildren are in the prime of life.
This is not surprising to an Objectivist. Objectivism
notes that wealth is created by human rationality and productive work. Wealth must be earned to be kept. Those who could not earn it, by and large find themselves unable to keep it.
Perhaps in a culture of rational individualism, this might change in one respect: if people begin leaving bequests to heirs chosen for their merit, and not their genetic relation to the giver, perhaps then wealth would accumulate across chains of heirs over time. But the result in that case would not be plutocracy, but a society characterized by the pyramid of ability.
Thus inheritance should be legal, out of respect for the rights of the living. Heirs deserve no great credit for what they inherit, but they will show by what they do with their inheritance how much they deserve it. Of course, no one is entitled to inherit, and I have no idea what the Objectivist view should be of people who die intestate (without a will).