My question involves criminal law for the state of: New York (specifically, Long Island)
So, obviously I made the stupid choice from attempting to steal stuff from a Target. I was of course, was caught and brought into the back room for questioning. I had nothing to hide, I confessed to stealing and was given the price on how much all of what I was attempting to steal was (It was under 100 dollars). They then took down my Name, Phone number and address, and told me that the police would not be notified, that I was banned from that specific Target store (but not any others) and that they would be sending me the civil demand in the mail, which I do intend on paying off no questions asked. Needless to say, this is never going to happen again.
My questions are: What kind of crime is this considered? Where is the information that I gave them going? And also, what is the payment process for these kinds of fines like?

