I don't know the story of how it came to be broken up into pieces, but as to it being a pious myth, I believe there are far too many miracles associated with the pieces of the true cross right through church history for them to be pieces of a simple lump of wood. I can think of the case with Saint Nektarios of Pentapolis, and also one of the nails which ended up on the island of Thasos. That's all I can recall at the moment, but I know I have read many other accounts.
Christos Anesti! Christ is Risen!