I've never seen a dividend payout for an ownership

I've never seen a dividend payout for an ownership date in the past. Dividends for stocks are announced in advance with the ex-dividend date and the payable date specifically stated by the company. Whoever owns shares at the close of business on the ex-dividend date gets the dividend. Whoever buys shares after that date misses out on the dividend. Here's a brief explanation from the SEC website. There's a detailed example available if you click the link.

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Ex-Dividend Dates:  When Are You Entitled to Dividends

To determine whether you should get a dividend, you need to look at two important dates. They are the "record date" or "date of record" and the "ex-dividend date" or "ex-date."

When a company declares a dividend, it sets a record date when you must be on the company's books as a shareholder to receive the dividend. Companies also use this date to determine who is sent proxy statements, financial reports, and other information.

Once the company sets the record date, the ex-dividend date is set based on stock exchange rules. The ex-dividend date is usually set for stocks two business days before the record date. If you purchase a stock on its ex-dividend date or after, you will not receive the next dividend payment. Instead, the seller gets the dividend. If you purchase before the ex-dividend date, you get the dividend.

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http://www.sec.gov/answers/dividen.htm