Advice please on baby Gladioli!
 

I planted some gladioli last year but this year I noticed hundreds and hundreds of tiny ones growing all round the original corms (I didn't lift them after they had finished last year). I have no idea what I should be doing with these tiddlers! If I leave them in situ do they affect the adult plants? Should I dig them up, transplant them, leave them, remove the original ones...?? Any advice would be gladly received, I am not much of a flower gardener! Thank you.