The white scented ones I leave in the ground all year and thin as I do Muscari (much muttering and patient weeding). The coloured ones I usually do in pots and I leave them in the pots with only whatever rain falls over the summer to maintain some soil moisture until late summer.

At which point the spawn usually falls free to be grown on and the larger bulbs can be planted up to produce their display.

They do well in river silt soils. The taller varieties benefit from added supports - whether other plants or 'gardeners' aids for upright growth' (twigs, stakes, mesh, wire...that stuff.)

If you have sneaky frosts - the long stem, coloured varieties do appreciate the shelter of a stone or brick wall and a south aspect otherwise both rain and frost mush the blooms.

I keep mine in a large pot, about 14 inches, year around. After the bloom I put the pot in a shady place until they start to grow next year. When I see new growth I begin regular water and fertilizer. They are now just finishing their bloom. Al

but what about the offshoots, should they be left on or removed and let them grow by them selves

You can separate and plant them. They will not usually bloom for a year or two, but they will grow and get bigger. They will do the same thing if you don't separate them, its your choice. Al