Once your letter is received by Membership records, they will send you a letter back confirming that they have received your letter. You will be told that your resignation is an "ecclesiastical matter" that must be handled by "Local Priesthood Leaders". This is their way of stalling in hopes that you will change your mind.
Your confirmation letter will also state that your temple blessings, priesthood authority and any and all blessings will be in effect canceled if you should proceed.
You may also receive a color or black and white (photo copied) pamphlet entitled, "An Invitation". It is a folded letter showing a picture of the current First Presidency of the Mormon Church. It will also tell you to please come back and "feast at the table" of what you once "knew". This is yet another attempt at inducing guilt on an emotional level. You can do as others have done - either keep it, or toss it in the garbage. We would provide a picture of the pamphlet, however, Intellectual Reserve (the strong legal arm of the Mormon Church) would sue us to have it removed.
Mormon Membership Records will forward your request and a name removal request to your local Bishop and/or Stake President. If you have moved several times, or have not stepped foot in a local Mormon Ward House in years, Membership Records will forward your request to the Mormon Church within the boundaries of where you currently live. Most likely if you are a current Member, the Mormon Church has long since found you and forwarded your membership records to the local Ward House. The Mormon Church has hundreds of senior citizens who have been "called" on a mission to the Salt Lake City Mormon Church Headquarters, to serve as "trackers". Their job is to spend all day tracking down wayward or otherwise missing members and to try and reactivate them. They do this by calling and misrepresenting who they are, or postal forwarding, or even contacting members of your family and having them "rat" you out. The Mormon Church is very persistent in trying to track down members and reactivate them.
It is important that the letter you receive from Membership Records is kept. This is your legal proof that they received your letter and are processing your request. In the United States, you are legally no longer a member once they receive your request. And regardless of what the Mormon Church has to do in an "ecclesiastical matter", you are officially resigned. You should keep this letter since many Bishops and Stake Presidents purposefully stall. Any time you need to contact Membership Records, you will have this letter as proof of the filing date.
As soon as you receive your "Please Come Back - This is an ecclesiastical matter" letter - you are LEGALLY no longer a member (Please note: This only applies to the United States of America. Please review your local laws on this matter). However, until you receive your final termination letter acknowledging that your name has been removed - you will still be considered a member of record. Therefore you should pursue your name remove/resignation until you receive this final confirmation letter.
Once you have received your termination or final confirmation letter - you should be completely free and consider that your name has indeed been removed. You will no longer be tracked and your membership records will no longer be sent to any local ward in the boundaries of which you live. NOTE: If you do not pursue the final termination/confirmation letter - then you will be considered a member and you will be hunted down indefinitely by the Church for reactivation attempts.
NOTE: Removing your name from the records of the Mormon Church will stop most all contact from local Ward members. If you live around Mormons it is inevitable that they will pursue you as a neighbor. This is an unfortunate side effect of being Mormon - every member is a "missionary". Also know that while your name is considered "removed", you will still be counted among the alleged "14+ million" members until you are 110 years old.
Be persistent! The Mormon Church is a huge corporation with thousands of gears. It moves extremely slow, especially if you are trying to have your name removed.
You also may receive a letter of confirmation the local Bishop or Stake President that they indeed received your letter, and that they are processing your request.
Realize that the Mormon Church could simply remove your name immediately and make the process faster, however, they do not. It is one more control issue the Mormon Church exercises upon the members - and this is to make you fit within their time frame. You have fit within their time frame long enough - time to take your life back!