It does spread slowly - every year I add more compost to the top of the raised area where my asparagus is coming up, and the area gets larger with each growing season.
Also, the asparagus roots you purchase to plant are supposedly only male plants. My asparagus has female plants so I have lots of seeds and they do sprout every spring. I have difficulty avoiding pulling or stepping on them when they're in other parts of the garden, but in that sense, the do "spread like weeds."
_________________ Northwesterner
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