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Providing these are regularProviding these are regular potatoes and not sweet potatoes (which are always vining), it might be more unusual to see them growing along the ground (unless they were just so heavy that the stems fell over) since they usually show an upright and bushy habit. We've read though that they might tend to vine more in cool climates, such as in the mountains of South America. We're guessing that it might also depend on the variety.   Not all potato plants flower; you still might get potatoes under the ground. Check carefully in the soil to see if you feel any potatoes developing.