no, conviction is the outcome of the arrest.
So in your case you were charged with Penal Law #xxx.x (misdeameanor) possesion of a control substance.
Your "conviction" is what you agreed to at your sentencing. example jail or probation for x amount of time. In your case (Conditional discharge)
you can read this.................................
http://www.uscis.gov/ilink/docView/S...-0-0-5667.html
Read section (a)(2)(B)
(B) Controlled substances.-
(i) Conviction.-Any alien who at any time after admission has been convicted of a violation of (or a conspiracy or attempt to violate) any law or regulation of a State, the United States, or a foreign country relating to a controlled substance (as defined in section 102 of the Controlled Substances Act (21 U.S.C. 802)), other than a single offense involving possession for one's own use of 30 grams or less of marijuana, is deportable.
section 102 of the Controlled Substances Act (21 U.S.C. 802)),
http://www.law.cornell.edu/uscode/21...2----000-.html
Now Im gonna tell you my own experience .. I was charged with Possesion of marijuana I had 2pounds.. ..so I knew that I had to get a lawyer no matter what. Question is how? and who to trust?? I first called around diffrent immigration lawyers looking for the ones with free consultation they all kept telling me I need a lawyer with experience in deportatin and criminal law .The problem is that I had to pay $80 + per consultation. So with that being said. I said to my self Im gonna read read read and read until I figure out my next step. So I came to this site. No one here gave me a straight answer So I kept searching and googling reading articles and immigration laws. After a while I ended up hiring a lawyer who I was confortable with for a second. Once I hired her i still had 2nd thoughts, I was scared for my life and my kid and my wife, shoot I still am!!!!. SO I ended up getting a second opinion then a third opinion and a forth. yes I know it sounds crazy and I did spend alot of money but >>> I got my answer. (Since I was a minor, My conviction is not considered deportable) Then one day while i was reading up on an article online I saw a link for
http://www.immigrantdefenseproject.org So i decided to send them a looooong email. They got back to me in less then a week and they helped me out ssssooo much . They provided legal help for FREE and they are very accurate. They are well respected in NYC and everyone i sent to them always thank me for letting them know about this group. I would say call them @ 212-725-6422, explain your story. I can almost guarantee you they will help you get all your answers. and if that doesnt work, then go the "spending money on many lawyers route". Eventually you will hire one, so be prepared to spend $ anyways but not right away. If you got ur GC in 2000 I guess it wil expire this year.. Dont rush into renewing it. if it expires , you r still a Resident.
Just dont get into any more trouble AT ALL.