Standby Guardianship
Not that I know diddly-squat about Ohio state law, but I did find this via Google:
"I. Designation of Standby Guardian
In Ohio, the main way to nominate a guardian for children has been through a Durable Power of Attorney. Therefore, it is in the commercial code that standby guardianship is described: "the power of attorney shall become effective at a later time or upon the occurrence of a specified event, including, but not limited to, the disability, incapacity, or adjudged incompetency" of the parent. [Commercial 1337.09(B)] However, lawmakers also have provided in the "guardian" section of the probate code a way for a parent to nominate a standby guardian in any other written attested document. [Probate 2111.121] Whether through a Durable Power of Attorney, or through another kind of attested writing, the emphasis is on the occurrence of a future event that begins the guardianship. The event need not be incapacity or disability.
Such a nomination amounts to a preference for the court to consider. A child 14 years or older also may express a preference, but the parent's nomination would tend to carry greater weight with the court. The law is clear, however, that the court ultimately will make an independent judgement about what is in the child's best interests. [Probate 2111.02(D); 2111.12]
The parent is free to design the terms of a designation – whether it shall apply to both the child's activities and property, or just the activities; when it shall commence; who the guardian shall be; whether it is to include unborn children; and how long it shall last. [Commercial 1337.09; Probate 2111.121] The parent likely will require the help of a lawyer to work out a designation plan for her children unless the Clerk of the Court has very clear forms.
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II. Agreement of the Non-Custodial Parent
There is no requirement that the non-custodial parent sign the nominating document. The standby guardianship laws do not describe requirements for finding and obtaining the consent of the non-custodial parent. However, other parts of Ohio law lay down specific factors for determining from whom consent needs to be obtained. For example, the adoption laws exclude the following kinds of parents from having to consent: those who have "failed without justifiable cause to communicate with the minor or to provide for the maintenance and support" for at least the preceding year; a putative father who fails to register as the father within 30 days of the birth; or who has willfully abandoned the mother during her pregnancy; or whose parental rights have been terminated; or who has been "judicially declared incompetent" and failed to respond to a request for consent; or one who simply fails to respond to the request whether or not incompetent; or wherever it is "unreasonably difficult" to obtain the consent, whether because of prolonged absence, unavailability; or any other reason. [Adoption 3107.07]
In other words, a non-custodial parent who demands preference over another nominated guardian, will have to have already expressed his willingness and ability to parent."
http://standbyguardianship.org/national/oh.asp
Here's the link to the actual code itself:
http://codes.ohio.gov/orc/2111.02