If a company splits its stock, there will be no gapping of the stock due to the split itself. A stock split does not materially affect a company's value and will not lead to the wide changes in value that are seen in gaps.
A stock split simply means that a company has increased the number of outstanding shares by the split factor. For example, if you hold 100 shares worth $1,000 in a company that undergoes a 2-for-1 stock split, you will hold 200 shares after the split. Before you get too excited about that possibility, keep in mind that the value of your position will remain the same. Instead of 100 shares at $10, you will have 200 shares at $5 after the split. This is where the confusion between a stock split and a gap comes in, since the price will fall from $10 to $5 at the time of the split and the change will be instant.
On the other hand, when a gap in a stock occurs, it means the stock's price has either increased or decreased sharply with no trading occurring in between. On a chart, this abrupt price movement will form an empty space or break between the prices. For example, let's say that the stock of XYZ has closed at $10 one day. After regular trading hours, the news comes out that the company might file for bankruptcy. At the start of the next trading day, XYZ's stock starts to trade at $5. This sharp decline means there is a large gap between the two days. In a 2-for-1 split, however, the price of the share declines by 50% but the value does not decline, so there is no real gap.
The reason gaps are not seen in stock charts after a stock split is because all of the past price data is adjusted to the current split. If you download the historical data of a stock, you will often see both the adjusted and the unadjusted share prices. In the event of splits, the unadjusted data will show gaps at each point the company split its shares. All the charts you see on financial websites should be adjusted for all past splits. Consider, for example, this chart of Apple Computers as it went through a stock split in Feb 2005.
The chart you will see on any financial site after a stock splits is represented by the red line. This represents the split-adjusted share price. The blue line represents the unadjusted share price of the stock after the split. The large drop in the blue line is the point at which the shares in the company split, causing what looks like a gap. The shares were trading at roughly $90 before the split and $45 after the split, cutting the price of the share in half. What the chart with the adjusted price does is divide all of the past prices by the split factor, making it look as though the split never happened. Note how at the start of the chart above, the blue line (unadjusted) is at roughly $30. The red line, which reflects all of the past prices on a split-adjusted basis, starts at roughly $15 (equivalent to $30 divided by the split factor of two).
The bottom line is that a stock split causes no change in the value of a company or in the value of an investor's shares, nor does it cause any gaps in a stock's chart, because past price movements are adjusted for the split.
(For more on stock splits, see Understanding Stock Splits.)