@SlightDelay
This been asked before.
If you have a partner you are not single. Doesnt matter if he is their dad or not.
If you have no man or woman in your life as a partner and you have children you are a single parent.
I have seen mums with boyfriends still saying they are single mums
but havent seen someone saying or thinking they arent a single parent because the ex is very involved with the children. Whether the parent is a dead beat or hands on is irrelevant.
So if you have 4 kids with an absent father, and a long term partner who doesn't share your house (or shares only part time) and doesn't financially support the children or play a parent role, you are no longer a 'single mum'?
Single mum does imply primary care and living alone, but it doesn't help anyone to police the term. I think if you have a live in partner who is sharing bills and taking an active role in the childrens' lives, whether a biological parent or not, you are no longer a 'single mum'. Or if you have low custody and the other parent is primary carer.
Everything else is up for debate. Men never hesitate to describe themselves as a 'single dad', even if they see the kids every other weekend, send the kids home with everything unwashed and keep missing both birthdays CMS payments. Give single mums a break.