Trust vs Probate

What is the name of your state? New York

My father's assets were held in a living trust, and his will was prepared
in conjunction with the trust agreement. He died two years ago. Since his
death the lawyer for the estate has been filing documents with a Surrogate's
Court in New York. Since I had previously thought the purpose of a Trust
was to avoid probate, and I'm confused as to the role of the Surrogate's
Court.

-Is filing with the Surrogate's Court the same as probating the estate (in
New York State)? Was my original assumption that the purpose of a
trust is to avoid probate correct, and if so, does filing with the Surrogate's
Court defeat the objectives of the Trust?

-I am a beneficiary of the will, but I have not received copies of the documents
filed with the Surrogate's Court. Should I be receiving filings either from the
filings either from the lawyer or direct from the court?

I would write that attorneys office and request a copy of everything, will and trust. You can also contact the ocurt and get a copy of what has been filed. The trust and will are separate and the attorney can tell you how to contact the trustee. You need to follow up on this immediately.