REDMOND, Wash. — NBC News has acquired full control of msnbc.com and its digital network from Microsoft Corp. and is immediately rebranding the site as NBCNews.com. Many details of the arrangement remain to be worked out, and financial terms weren't disclosed. But NBC News President Steve Capus said the site — one of the news industry's earliest and most successful online operations — would become part of NBC News Digital, a new division led by Vivian Schiller, the former president and chief executive of National Public Radio. Schiller joined NBC News as chief digital officer last year.