Gift tax in the United States
If a person is a non-resident alien for purposes of gift tax, taxation of gifts is determined in a different way. If the property is not located in the U.S., there is no gift tax. If it is intangible property, such as shares in U.S. corporations and interests in partnerships or LLCs, there is no gift tax.
United States trust law
Fiduciary tax law is both federal (see the Internal Revenue Code) and state. For Federal income tax purposes in the United States, there are several kinds of trusts: grantor trusts whose tax consequences flow directly to the settlor's Form 1040 (U.S. Individual Income Tax Return) and state return, simple trusts in which all the income created must be distributed to one or more beneficiaries and is therefore taxed to the non-settlor beneficiary (e.g. the widow of a trust created by the late husband), whether or not the income is actually distributed (it happens), and complex trusts, which are, in general, all trusts that aren't grantor trusts or simple trusts. Some trusts may alternate between simple and complex under certain conditions. Many but not all trust organizations do their own tax work. This can be highly specialized work.