Since your ex's great nephew is now 19 years old, this would be considered an 'adult adoption' . . If this matter was in Illinois, you would be allowed to adopt your ex's great nephew since you have had physical and legal custody for more than 2 years; and under Illinois law, you would not need the biological parents' consent, but the adult being adopted would have to consent to his own adoption as part of the process. Since adoption laws vary from state to state, you should contact any attorney in your area who is familiar with adoption laws to determine what is needed.
In California, adult adoptions are governed by California Family Code sections 9300-9307. The filing requirements for each county differ, though generally a Petition for Adoption and Adoption Agreement will be required, as well as a final Adoption Order which the judge will sign. If either you or your ex-husband's great nephew is married, the consent of your respective spouses may also be required. The process is fairly straight-forward and it is possible that you will be able to complete it yourself. I recommend you contact your local Superior Court to determine what forms or pleadings are required. If it becomes overwhelming, research a local adoption attorney who will likely be able to assist you for a relatively low rate based on the simplicity of the matter.