From the link below, the author stated that it is not hard to grow a new plant of cyperus papyrus . Seems to me, just a cut stem can induce roots and becomes a new plant. Your new plants probably produced through this way, a broken stem induced roots and become a new plants.
From the link:
"Start new plants from the tip of the stem. Cut off the top few inches of the stem and place it upside down in a glass of water or well drained potting mix. The leafy stem tip will be in the water or potting mix while the leafless stem points upward toward the ceiling. Roots and new shoots will form over the next few weeks. Soon you will have a new plant to share or add to your indoor garden."
Looks more like Typha to me... we really need to see the tops of the plants for a full ID. Typha really like higher nutrient levels and is a regular in storm water run off drainage.