If the father of my children has not seen/talked my kids in over a year, nor has he paid child support, what do I have to do to remove his parental rights?

Simply by remaining absent fromthe child's life for over a year and defaulting on child support will not be enough to carry the extremely high burden of proof for termination of his parental rights.  Most courts require termination to be combined with adoption.  Children need a father.  Just because he's totally blowing off his responsibilities as a father at this time, that will not be enough to persuade a judge to terminate his rights.  Many family lawyers refer to termination as the family-law equivalent to the death penalty--it's the harshest penalty in family law, and for good reason. 

Now, if he starts coming back around, it will be appropriate (some might say it's your obligation) to file a motion to modify conservatorship in order to prevent him from jumping back into the kids' lives and confusing the heck out of them.  If they're small, the kids will be confused and may be emotionally harmed by him just coming back in, without him first being vetted and evaluated to make sure he's responsible and morally-oriented enough to know how to meet their physical and emotional needs during his possession times.  Often, when a parent comes back after being absent, courts order "stair-step" visitation, where it starts out for a few weeks or months under supervised visitation, then gradually relaxing the restrictions IF the parent goes through all the steps.  This permits him to get to know the children again gradually, lets the children warm up to him at an age-appropriate pace, and puts the ball in his court to prove that he can follow orders and act in their best interest.

So, if he starts coming back around, asking to have his possession periods, get as much information as you can about his goings-on.  If he's unwilling to give you the straight dope on what he was doing all that time, and why he was absent, you should smell a rat.  If he starts acting like he'll stand on his rights and try to get the kids out of school or bring a constable to your door, hire an attorney, file for modification of the parenting plan, and get a TRO against him until you can get a hearing.

As far as what to plan for in the event of your death, that's more than I can go into here, but if you'd like a brief, no-cost phone consultation, feel free to contact my office.