Can I file my own petition for divorce for abandonment?

In Arizona the grounds for a dissolution of marriage are that the marriage is irretrievably broken, with no prospect of reconciliation. You are always best served by at least consulting with an experienced family law attorney in your area, but you may file your own petition using the self service center at the superior court location near you. Maricopa County also provides online access to its self service center. Here is a link: http://www.superiorcourt.maricopa.gov/SuperiorCourt/Self-ServiceCenter/Forms/FamilyCourt/

Yes. Try SCAO forms in Michiganan look online.

Yes, you can file for divorce on the basis of abandonment, although you can file for divorce without having any reason at all in Utah. I am not aware of a prefabricated form that exists for filing for divorce on the basis of abandonment, but as I previously stated, if you want to get a divorce you don't need to plead abandonment or some other fault-based ground. If you are looking to file for divorce on your own, in a do-it-yourself fashion, you may wish to start with this link: http://www.utcourts.gov/ocap/utah/divorce/. It's a link to the Utah Courts' forms for a do-it-yourself divorce. The forms are not completely free; you will be charged $20 for using the service, but this is the cheapest do-it-yourself Utah divorce website I know of.

Abandonment is not grounds for dissolution of marriage in Florida.

Abandonment is not relevant to divorce in California. If you want a divorce you can file papers and claim irreconcilable differences.