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This is called a contingency fee agreement.
The attorney's portion need not be 50%, as that can be negotiated. Many will charge 30% for services, and 40% if it goes to trial (versus settlement).
An attorney can be located here:
You would choose the area of law (ie personal injury, general civil, etc) and then contact the firm of choice to see if they accept contingency fee cases. This is most common in personal injury cases.
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