My son's best friend has lived in my home and I have provided total support for him since August 2011. He has contact with his family, via the cell phone in which I provide for him, but they do not financially support him and very rarely see him. The mother receives child support from the father for him and I also believe they receive state benefits from the state of Texas, where we live. Will I be able to adopt this child or at least apply for guardenship? What will the process be?

How are you caring for this child when you have no legal right to? What happens if he needs medical treatment? You have no right to authorize it.

The parents are breaking the law if they are receiving benefits for a child not living with them!
You could be in trouble for parental interference if you do not have permission to harbor this child.

What you need to do, is report the situation to family services and inform them you are willing to foster the child.

... Will I be able to adopt this child or at least apply for guardenship? What will the process be?

Yes and yes.

I suspect that if you go for adoption a home study, probably at your expense, will be required. The parents will also have to agree.

You need to consult a Texas attorney for the details.

... How are you caring for this child when you have no legal right to? What happens if he needs medical treatment? You have no right to authorize it ...

That would be a different bridge to cross. In an emergency, treatment can probably be given if necessary.

The grandmother of the child, whom lives with the custodial mother, went and signed at the school that the child lived with me "also". Therefore, I am able to pick the child up from school and all of his teachers call me if they need something. The one time that the child has needed medical attention for allergies, he went to the clinic at the school and they called in a prescription that I paid for out of pocket. You are correct, If something dangerous should happen, I have no authority, and this is a constant fear of mine.

You can try applying for guardianship. But I think the court will ask a lot of questions that you don't have good answers for.

Actually grandmother has no legal right to do that, only the mother or father the person with legal custody can sign. In fact someone would have to sign for the Grandmother to pick up the child also.

So you have no legal right to put the child in school or send to the doctor.

In fact the parents could sue you if something happened to the child.

To adopt, the mother and father will have to sign to allow the adoption.