The most consequential thing about the standard is when it is measured. Utah's text says the testator must have capacity "at the time that the will is executed," and its presumption in subsection (4) runs to "the time that a will was executed." Capacity is a condition at a moment, not a status held over a period. That single feature explains most of what looks paradoxical in this area. A person with a progressive illness may lack capacity on many days and have it on the morning they sign. A court asked to decide the question does not ask whether the testator was generally well; it asks about the signing. The practical consequence for a family is that the useful evidence is contemporaneous and narrow, which is why the lawyer's file notes, who else was in the room, and what the testator said about their own property carry more weight than a medical history.
The threshold itself is low, and that is deliberate. Read Utah's four parts as a list of what is not required. Nothing asks whether the plan is sensible, fair or consistent with what the testator said last year. Nothing asks whether the testator could manage a portfolio, run a household or balance an account. Subsection (3) removes an item people assume is in there: "A testator is not required to have any knowledge or understanding of the laws of inheritance by intestate succession." Minnesota's "sound mind" reaches the same place by a shorter road. The doctrine exists so that a person's own instructions govern their property, and setting the bar high would disenfranchise exactly the people most likely to be writing a will.
Subsection (4) is the sentence worth carrying away, because it corrects the belief that most often stops families acting. Utah provides: "There is a rebuttable presumption that testamentary capacity exists at the time that a will was executed even if the testator is subject to a guardianship or conservatorship or is otherwise unable to independently manage the testator's affairs." A conservatorship is a court's finding about the ability to manage property and business affairs on an ongoing basis. Testamentary capacity is a different question, asked about a different moment, for a different purpose, and the statute refuses to let the first answer the second. Published guardianship and conservatorship cover what those proceedings are and what they decide; what they do not decide is this.
Different instruments use different capacity tests, and they are not interchangeable. The Uniform Power of Attorney Act, in Maine's enactment, defines incapacity for its own purposes as an inability to manage property or business affairs because the individual is impaired "to the extent that the individual lacks sufficient understanding, capacity or ability to receive and evaluate information or make or communicate decisions" about those affairs, and the same definition separately covers being missing, detained or outside the country and unable to return. That is a management test written for an instrument that operates during life. A will operates only at death and asks the four questions above. Someone can fail one and satisfy the other, in either direction.
In a contest, the person challenging carries it. Minnesota's allocation is representative: proponents of a will must establish prima facie proof of due execution in all cases, and "contestants of a will have the burden of establishing lack of testamentary intent or capacity, undue influence, fraud, duress, mistake or revocation." So the will is not put on trial by an allegation. Note that the statutory list separates lack of testamentary intent from lack of capacity: intent asks whether the person meant the document to be their will at all, which is a live question for a draft, an unsigned copy or a letter, and it is not the same as asking whether they were able to.
One place where capacity and a drafting choice interact directly. California's rule for a holographic will that carries no date provides that if it is established the testator lacked testamentary capacity "at any time during which the will might have been executed," the will is invalid unless it is established that it was executed at a time when they had capacity. A will's date is usually treated as a formality. On an undated handwritten will, in a state with that rule, it becomes the thing that decides whether a capacity challenge can be answered at all.