They chose to give up on them by entrusting them voluntarily into my full care. I guess the better way to word it is that they gave up the responsibility of joint parenting.
I don't agree with this statement.
Just because you are the primary parent, and probably could win sole custody if you did fight for it in court, does not remove their natural right of the other parent to joint custody.
In other words, until a court orders that you have sole custody, you don't. The actions of your ex's may sway the courts to grant you sole, but do not amount to an automatic release of rights.
You ex's have as much entitlement to the kids as you do, notwithstanding you doing the majority of the parenting. The children are entitled to a relationship with both parents, and it is commonly held that it is the responsibility of the custodial parent to promote that relationship, as that is what is in the children's best interests.