Certainly the legal situation is that you don't have a right to know. The fact that your bf's ex has custody means that she is responsible for the care of the child and that includes who lives with the child and who the child associates with.She doesn't have to tell you unfortunatly but there are obviously ways you can find out, but that won't get you any further as if he is something like a paediophile then there's no way you would know. You can't run a check of any sort on him without his consent which under the circumstances since your bf and his ex appear on such bad terms seems unlikely to say the least. Your best bet in getting any sort of idea ABOUT the man, ( and I don't mean his name and statistics) is by talking to the little un. You'll soon get an idea of whether she likes him, and if he's a decent person by chatting to her and that's all that should really concern you. If you do get a name what possible good will it do you, as you won't be any further forward and I think your bf's ex will just see it as an intrusion and you trying to be controlling of her.You need to just try and guage the TYPE of man he is, and if the little un is comfortable with him then try and relax, you'll find out his name eventually. If she's not you need to discuss this with your bf's ex as that should be a cause for concern to all especially her mother.It does seem stupid not telling you, but the info is of no use to you anyway and it all just seems like a power struggle to me which is a shame for the little girl involved.