Transplanting a Phormium

We've found a Phormium growing in our garden, obviously from seed and it's now about 1' high. I want to move it it a more suitable space before it gets too large & would like to know the best time of year to move it.

 

Do phormiums self seed?

I've grown then from seed, but I'm just wondering how common it is for them to self seed.

 

Self-seeding Phormiums

At first I thought it was a species of grass but it is now in its second year & I'm 99.9% certain it's a Phormium. Perhaps birds eat the 'fruit' that forms after flowering & the seeds pass through the birds?

 

Possible polypody.