I had a detailed post that got eaten, so I'm going to chime in briefly:
An involuntary TPR is doable, on grounds such as abandonment or failure to assume parental duties. Each state has its specific process and grounds--here in WI, I did an involuntary TPR pending adoption (by grandparents; Mom was deceased) on a biological father who had never met his daughter (Mom and dad had a single encounter and were never in a relationship), so we did both the above grounds. All we had was a name. We had to send notice to his last known address (which we didn't have, so we couldn't do--we did some cursory digging but didn't have to pay a PI to track him down or anything; it's unlikely he even knew his daughter existed) and publish notice in a newspaper serving that location (which is what we did do). The judge considered all of this, interviewed the daughter (who was 14 and thus legally got a say) and a guardian ad litem (GAL) (appointed to represent her interests), would have interviewed Dad if he'd showed (to give him a chance to explain why retaining his rights would be in the girl's best interest), and provisionally terminated Dad's rights, subject to a 30-day appeal period. (Your daughter's father would be served in prison, and may be asked to testify by phone.)
We came back after the appeal period (not surprisingly, Dad did not appeal) and the TPR was finalized, and the adoption proceeded that day as well.
As for costs, or a relatively uncomplicated TPR and adoption, I'd probably ask for a $1,500 retainer (my rate is $180/hour--family law attorneys can cost between $125-$300 an hour or more), and, if the process stayed uncomplicated, I probably wouldn't exceed the retainer (though, say, if bio-dad showed up and started making hay, it could get expensive quickly). There'd also be the cost of filing the court action ($10-$100, depending on the court), service of process or publication of notice (free to several hundred dollars, depending on whether you can just get a friend to drop off papers versus having to pay a process server or publish one or more notices in a newspaper) home studies (stepparent adoption home visits are pretty basic or waived altogether in some states, so costs can be anywhere from nothing to several hundred dollars; the assumption is that the stepparent already lives with the kids anyway, and is married to the biological parent, so it's not like a whole lot would change at home if the adoption was granted); GAL fees ($450 retainer in my local court); revised birth certificate ($40); miscellaneous charges for postage, faxing, long distance, etc. So, a few grand, give or take.
Best of luck!
ProtoLawyer (the now-actual lawyer, this isn't legal advice, please don't take legal advice from some anonymous yahoo on the Internet)
Spouse (the political geek) * Stepdaughter (the artist) * and introducing...the Baby (um, he's a baby? He likes shiny things).