An heraldic bucket shop is a heraldry company that will "sell" a coat of arms associated with the customer's surname, regardless of whether the customer can actually claim a relation to the original armiger.
According to the law of arms, usage of a pre-existing coat of arms must be predicated on some form of relation. Typically, inheritance of arms flows through the male line though in many traditions, it may flow through the female line as well.
Bucket shops work from a pre-built database of surnames and shields that were sourced from manuscripts, armorials and various journals. Using a database such as this, the seller may sell to anyone named, for example, "Smith" the arms found for another Smith. Unfortunately, the chances of any relationship with the original "Smith", let alone patrilineal descent, are slim to none.