so once all outstanding stocks are bought is a company marketcap 0

Here is my short answer, than a better answer from Wiki:
There is never a time when all outstanding stocks r bought in a company, while it is trading. Therefore, the market cap is never 0. If u have a bankrupt company that stopped trading, perhaps u would consider that a 0 market cap.

from Wikipedia:
Market capitalization represents the public consensus on the value of a company is equity. A corporation, including all of its assets, may be freely bought & sold through purchases & sales of stock, which will determine the price of the company is shares. Its market capitalization is this share price multiplied by the number of shares in issue, providing a total value for the company is shares & thus for the company as a whole.

Many companies have a dominant shareholder, which may be a government entity, a family, or another corporation. Many stock market indices such as the (S&P 500, Sensex, FTSE, DAX, Nikkei, Ibovespa, & MSCI) adjust for these by calculating on a ''free float'' basis, ie the market capitalization they use is the value of the publicly tradable part of the company.

Note that market capitalization is a market estimate of a company is value, based on perceived future prospects, economic & monetary conditions. Stock prices can also be moved by speculation about changes in expectations about profits or about mergers & acquisitions.

It is possible for stock markets to get caught up in an economic bubble, like the steep rise in valuation of technology stocks in the late 1990s followed by the dot-com crash in 2000. Speculation can affect any asset class, such as gold or real estate. In such events, valuations rise disproportionately to what many people would consider the fundamental value of the assets in question. In the case of stocks, this pushes up market capitalization in what might be called an ''artificial'' manner. Market capitalization is therefore only a rough measure of the true size of a market.

No. The market cap is not zero. Someone owns the stock, whether it is all sold to the public yet or not. This is based on the value times the number of shares, not who owns them at a given point in time.