Mr. Cash, yes and toppcats dilutional factor, although a great point, doesn't change the fact that splitting a stock does not change the zero-sum.
A stock is only worth what I can sell it for. If abc splits 3 for 1 the new shares are worth 1/3of the old ones...doesn't matter who holds them. Bottom line someone has to SELL them before we can determine their worth and that means someone has to BUY them.
Zero-Sum does change however over time due to the injection of liquidity into world systems. For example: the creation of funds by the FED. The trade off is they must SELL debt to finance the liquidity.