My Aunt has stomach cancer and is currently dying. She has three girls, One of them is 18 and the other two are 13 and 14.

Even though your aunt as appointed another family member to be the children's guardian, the children's father(s) would have first right to take the children.  In the event that the children's father(s) are around, but they are not fit to care for the children, then there would a custody battle between the father(s), proposed guardians in the will, and (possibly) the 18 year old sister. Your cousin would have to petition the court, upon the death of her mother, to be her sisters' guardian.  Testamentary appointment of a guardian, as outlined in Arizona Revised Statute 14-5202, usually will control.  However, your 14 year old cousin, under Arizona Revised Statute 14-5203 has the right to object to the cousin being her guardian.  This objection has to happen before the cousin's are appointed as his/her guardian.  This objection will prevent the appointment from going forward, but it does not bar it completely.  The 13 year old, once she turns 14 can object to either the appointment being made (provided she is 14 at the time) or can petition to terminate the guardianship appointment. If the Court was to consider your cousin's Petition to be her sisters' guardians, she would need to show that it is in the children's best interest to be place in her care, custody, and control versus the proposed guardian.  Basically she would have to show that she is a more fit placement than the proposed guardians.  She would have the burden of proof in that case. *This answer is for informational purposes only and does not create an attorney-client relationship between the question presenter and Laura B. Monte, Esq. or Donaldson Stewart, P.C. * *Laura B. Monte, Esq. is only licensed to practice law in the State of Arizona.*