Even within the big-3, the dominance has changed. A decade or two ago, the BCCI, ECB and CA all had equal importance and strength. But once the IPL got established, the BCCI has managed to move ahead and carve a place for itself. Now the other two boards are dependent on the BCCI for a large share of their funds. Even their T20 leagues (Hundred and BBL) attract a lot of revenue from India. When Shashank Manohar was the chairman of the ICC, he took some strong steps to reduce the dominance of the BCCI. But now everything is back to ground zero, ever since the useless businessman Greg Barclay took over.
One thing I recently noticed is that Australia has made it compulsory for its players not to miss national team series. For the very first time Australian players are going to miss part of IPL due to there tour to Pakistan. If all boards take such decision we can definitely see less influence of BCCI. Its important for cricket that all boards must be at same level and all leagues must have same importance.