How do I get appointed as representative

Based on the next of kin, my Grand Uncle would have my Uncle and my Father as relatives. They both live out of state (Florida) where he died. They both want ME to start probate and to be the one who handles everything. What is that called? How do I get the process going? What do I need them to sign before I go to the attorney? Also - IF anything remains, then before we start the process we have all agreed that no matter who is named on the will (if one exists) that we will split it into three equal shares. What should we write up and sign (in front of a notary)? Is there a form we could use on-line? We don't have a lot of funds for an attorney to do everything. I'd like to have things ready to cut down costs.

This is one -- because of the distant family relationships and geographical distances (I gather) in which you would be better off starting with the attorney, explaining the situation, and then having the attorney get most of the things done for you.

Most attorneys charge based on the size of the estate, and if the estate is tiny, they don't want to waste their time or your money and will let you do, and tell you how to do the things you can effectively do yourself. For now, just a simple letter stating that in consideration of the cooperation and effort involved, regardless of what any one of the 3 might receive as a result of the death of Great-Uncel Joe, you'll total up what each of you receive and divide all the money and property by 3, with each of the 3 of you getting 1/3rd. All of you should sign, with each of you having a signed copy.