Specifically, which allium it is that will propagate itself though your garden? I am looking for one that is tall, round & purple.
I have Globemaster alliums in my garden. They are tall, round and purple. I got them as bulbs last year and they flowered well for me around May to June. I presume the bulbs will divide to produce new plants. I also left the seed heads on to see if they will spread that way too. The plants reached about 80cms in height and seemed to like my well drained soil. They also like sunshine but I found that if you planted them in partial shade the flowers lasted longer. It did say on the pack that they were valuable for planting in groups in borders or for naturalising and that they would flower year after year. Hope this helps you out.
I have 3 different kinds of alliums in my gardens. The biggest is Allium Christophii, which as blooms the size of dodge balls, then the Globemaster, and a smaller one, not sure the name, but I think it is called strawberry something LOL They all self seed, but it takes quite a few years before they bloom. If you want them instantly, best you buy some bulbs.
I also have many. Most ate globe master -the big bloom ones. I spray painted some of the dry blooms. Seen this at Iowa State fair. They had done it in red.