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They will not reseed, as males cannot produce seeds. They only produce pollen. They will still reproduce with their roots, though. They will spread in that way, rather than spreading by seed. Also, these will all be male, since they are just extensions of the same plant.
This article will help you with the care of asparagus: https://www.gardeningknowhow.com/edible/vegetables/asparagus/growing-asparagus.htm