Why did Constantine select the independent Catholic grouping in Rome and not the independent Catholic groupings elsewhere to formalize the Catholic Church under Roman authority?

Answer 1

You are confused, first of all, there is no "independent Catholic grouping", there is just the world-wide Catholic Church under the successor of St. Peter. Our Blessed Lord has only established One Church, and, as it is His Body, It will remain ONE until the end of the world. Secondly, Constantine did not select anything, and did not "formalize" the Catholic Church. All Constantine did was to make Christianity legal. The center of the Catholic Church as always been in Rome since St. Peter went there, and died there. Constantine legalized Christianity, but did not become a Christian, himself, until on his death bed.