Many parents will get insurance just on their kids. Sometimes the parents cannot afford to get insurance on themselves but want coverage on their kids. Sometimes the parents are uninsurable. Sometimes the parents are divorced; the kid lives with one parent but the other parent pays for the insurance. Sometimes the parent doesn't want insurance for whatever reason, but the kids needs it to play sports in school. Sometimes the mother is still on her parents' insurance policy (which is now allowed to age 26, another consequence of the Act).
Child-Only policies are no longer available. This is a direct result of the HealthCare Reform Act, also known as the "Affordable Care Act" which did little to making care affordable. A part of the bill stated that insurance companies cannot decline to accept any child because of a pre-existing health condition. Sounds good on the surface - who can really oppose children getting treatment? What happened in real life, however, is the insurance companies just stopped accept all children unless there was a parent or guardian also included on the policy.
The insurance companies did this to help keep premiums from increasing even more than they have. To get a policy by yourself you now must be age 19 or older.
If you need Child-Only health insurance there is one plan in Arizona that will still write a child-only policy. They will write Child-Only policies on kids age 2 through 18. The policy is a short term medical policy, and you can get more information here.
The problem with a short term medical is it doesn't cover pre-existing conditions and the policy will expire after the term is over (usually 6 to 12 months). You can reapply for another term upon expiration but any health conditions that may have developed during the previous term will not be covered. As an example, a child breaks a leg and goes to the ER to get it set. The policy covered the broken leg (after deductible) but terminated two days later. The parent applies for a new policy. The new policy will not cover the follow up visits for the broken leg, so the parent is now responsible for paying to remove the cast.
When you go on my website there will be one company that has 3 options. Give me a call with questions. As of now this is your only option other than through the state Medicaid department.