Once the grass turns brown it can either be removed immediately or removed in the spring. Where temperatures get colder than 35 degrees F, the plants should be treated as annuals.
King Tut is an evergreen or neutral grass. It is best to keep the soil moist, but once established King Tut has proven to be surprisingly tolerant of dry conditions. King Tut will also do well when planted in normal garden beds. If the plant is put into a pot I would suggest plugging the hole or holes in the bottom of the pot to keep as much water as possible in the pot. The root ball can be submerged but it isn't necessary. The purpose is to keep the bulk of the soil or root mass wet. The crown of the plant should never be covered in water and in fact both of these varieties can thrive in water as shallow as a few inches. The plant can be planted in pots, along the waters edge of a pond, or even in a pond. It is a very fast grower and will quickly grow to impressive size when replanted in the spring.
Cyperus Papyrus is not hardy enough to survive winters with freezing temperatures and it is not a candidate to overwinter inside.