
Yes, grandparents have rights in Arizona. In Arizona, grandparents can establish visitation rights if any of the following circumstances are true:
If the parents of the grandchildren are married to each other, grandparents cannot petition the court to establish any visitation. The reasoning behind this is that the courts will not "interfere" in existing marriages. This means that the married parents of the children can decide how much visitation time grandparents can have. It also means that if married parents decided to have no contact with the grandparents, there is little the grandparents can do legally, unless the parents are unfit for some reason, then grandparents may wish to file a dependency petition. Or if the child sees the grandparents as parental figures, they can file a Petition for In Loco Parentis (which in Latin means "stands in the place of the parents").
Assuming that the parents are not married to each other or the parents are divorced or one of the parents is deceased, a grandparent can file a Petition for Grandparent Visitation. Under most circumstances the court will assume that the grandparent can have access to their grandchild when their son/daughter has access to the child. However, there are circumstances when this is not possible: their son/daughter does not want the grandparent to have access to the grandchildren, the son/daughter does not live near the grandchildren (and the grandparents do), or the son/daughter does not see their children for one reason or another. There may be other reasons as well.
The court will not give custody to the grandparents under the grandparent visitation statute; grandparents must file an In Loco Parentis Petition for that, or a guardianship petition. The court will not give grandparents and a parent equal time. The court will give the grandparent some access, after first determining whether the contact is in the children's best interest, looking at the amount of time the parent(s) are actually giving to the grandparents, and the reason why a fit parent has decided to limit the access. In other words, a grandparent can obtain court-ordered time, but it may not be as often or as long as a grandparent may like. It all depends upon the facts and circumstances of hte case, and you may wish to seek legal counsel to assist you with this issue.
Grandparent rights come from the parent's rights. So if paternal grandparents are seeking visitation, the parties need to have been married, or paternity must have been legally established by the court.