I would like to know how to submit an application for Divorce due to abandonment. I have not seen/heard from my lawful wife in almost 10 years in NY.

In  order to proceed for a divorce based on abandonment, you must both allege that you have not seen or heard from your spouse for at least 1 year without justification and in order to obtain the divorce, prove to the Court that you have made a diligent effort to locate your wife and have been unable to do so. You would need to search public records and last known addresses to try to locate her.  You should contact an attorney in your area who is familiar with uncontested divorces based on abandonment. -Alfred Polizzotto, III