The IHT liability is determined by the Personal Representatives (executors or administrators) of the deceased's estate.
The rules are complicated, but the amount of IHT payable on the estate can be affected by gifts made in the preceding 14 years. Assuming that the deceased hasn't given away more than the nil rate band (currently �300,000) during that time, the recipients of any gifts in excess of �3,000 should not have to pay IHT. The effect of the gifts is to reduce the amount of the nil rate band available to the PRs, and thereby increasing the tax payable on the estate.
If you're talking about big gifts, in excess of �300,000, the recipient could end up with a bill for IHT. Again, the PRs should calculate the tax due.
LS