What is the complete definition for assault and battery high aggravated nature?

It depends upon the State in which the criminal complaint took place and the law used to indict you of the crime. The definition of a crime of violence for aggravated felony purposes depends upon the State statute as well as how the incident will be interpretated for immigration purposes. Your question requires more information and information on the actual level of contact and whether physical injury that took place for immigration purposes. If you have yet to be indicted or charged with a crime, then this is unclear. Did this take place in South Carolina or some other State? Do you have a copy of a police report? Perhaps, you should schedule an appointment or teleconference with an experienced immigration attorney. This will allow the attorney to spend enough time to understand the situation and refer you to a competent criminal attorney who will be sensitive to the immigration consequences of a criminal conviction and work with the immigration attorney for the best possible outcome. This is general information and does not create an attorney-client relationship.

One point, excuse the assumption, I don't know who may be charged with a crime.