Public companies don't really 'create' new shares. Occasionally they perform a 'share split' which does change the number of shares available but doesn't affect the ownership. No money changes hands.
It looks like new shares have been issued, but it's more like you are now able to sell fractions of shares, e.g., you own 10 shares in a corp representing 10% ownership (so there are 100 shares overall). Each share you sell represents a 1% stake in the company so you won't be able to sell 0.5% (half a share). A share split is executed. You now own 20 shares (out of 200) still representing 10% but now you could sell one new share (half an old share) representing a 0.5% stake.
In the Real World,
Stock Splits are thought to increase liquidity (ease of buying/selling) with a possible uplift to the share price. I'm not sure how the game handles this as fundamentally nothing has changed with the corp - the corp won't be any more profitable or productive after a split.
However, you can manually create shares (in a public corporation, click on 'perform a public offering'). This is a way of injecting cash into a struggling corporation or, if you want to increase your %-ownership and no-one is selling shares, you can dilute their ownership by issuing shares above market price and buying them up with your Enterprise.
A corporation can also withdraw (repurchase) shares if it has lots of cash to spare (that's the corp,
not the enterprise or majority shareholder). In this case, essentially the corp buys the shares and then 'destroys' them by not offering them up for sale. The %-ownership of all other share holders with increase slightly as a result.