This question has come up for years. I respond with the same answer over and over again. It won't happen.
With that said, I do agree that if Dividend splits start to occur again with other companies for whatever "emotional reason", that the post below does have merit. If IBM meets its 2015 earnings of at least $20 a share, then possibly at that time (2016) a Dividend split might occur.
IBM will not split the stock until they reach the stated goal of $20 per share. The dividend will increase, and my guess is $.95 per quarter from $.85 per quarter. Which is $3.80 on a yearly basis. Ya get paid to hold the stock. Kinda nice huh?