REITs don't "wash" money any more than any other investment. They declare a dividend each month or quarter and every year, they are obligated to pay 90% of their taxable income in dividends, then of course, they are not taxed on those payments, just the recipients are.
From an accounting standpoint, it makes no difference if you're invested in a REIT or Google, except that REITs pay a large dividend and Google doesn't. Though REITs have been poor performers for the last couple of years, while Google has done very well.
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