Will ornamental alliums become invasive?

I'm planning a garden from scratch (previously overgrown for years). I have several alliums in pots and was going to put them into the borders- sphaerocehalon, schubertii, gladiator and mohican. Should I used bulb baskets or are these varieties slow spreading? Any idea how long before they might need thinning out?

 

Don't know what it's called, but there's a pretty little pinky white one that is an invasive PITA

 

Thanks BB3. Hmm, none of mine are pink. I know wild garlic and three-cornered leek can be an issue, but unsure whether I'm starting my own PITA by planting these in the beds?

 

None of the ones you mention will cause you any problems in terms of unwanted spreading. Our tall Gladiator types have been in for 5 years now and are just about making clumps of 2 to4 flowering stems.
Removing the old flower stems before the seed is fully ripe would stop any of them seeding around too.

 

I found A sphaerocephalon spread itself around a bit too readily and I am still finding them over 10 years after deciding to get rid.

 

I agree - A. sphaerocephalon spreads very readily here, as opposed to most other alliums which can struggle to survive/thrive year on year. It's only in the past couple of years that conditions have suited some of them well enough here to grow.
Some will always do better than others, as it depends on the soil and climate.