If the father is not named on the birth certificate, you probably won't have any problems. I say probably, because I went through all this almost 3 years ago and things have changed since. My sons only have my name on their birth certificates, so I was able to obtain their passports, visas, and change their last name (which had been my maiden name anyway) to my married one. All without much fuss.
If your child's father's name IS on the birth certificate, you will need his permission to obtain the passport (assuming your child doesn't already have one) AND the visa. Regardless of whether there is any "paperwork."