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If you bought the assets of their business instead of the stock of the company then the company has the right to the tax ID since the entity has that unique number as your entity would have it's own. However, I think what you are trying to ask is if they can continue and compete against you after allegedly selling the business to you. The way this normally gets handled is in the Asset Purchase Agreement and the specific topic is called the noncompete covenant. This clause, if properly drafted, would have seller agree to not compete (and the seller's owners) against buyer for some period of years in some specified geographic area. If your purchase agreement did not address this issue then you a out of luck unless there are other provisions that you could allege were breaches of the agreement. As a last ditch effort, you could sue for fraud if they misrepresented the terms of the sale and how it was to be conveyed to youi....essentially a tort of fraud in the inducement. Best you meet with a business litigator to evaluate your ability to shut down the competing seller.
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