The correct statements that describe ways that Ivan III increased his power or status as ruler of Russia are:
- Russians were encouraged to believe that Moscow had become the new center of Christianity.
- Many Russian princes and boyars willingly pledged their support to Ivan III and turned over their land.
- Ivan III stopped sending tributes to the Tatar court.
The statement about deporting boyars he considered troublemakers may have some historical context, but it is not widely recognized as a primary method through which he increased his power, compared to the other options provided.