I'm lost... This bloke wants to see his kid? Clearly, why else would he be seeking custody?
You want to know what consitututes good grounds to stop him seeing his kid?
BUT - you wont tell us anything specific about what this bloke has done to give you grounds to think he should not see his kid???
So how does this work?
He applies to court, you tell the magistrate your story, he tells the magistrate his story, in all likelyhood a report will be ordered from a family consultant, you will be interviewed, so will dad. You will be observed with the child so will dad, the report writer will write a report to the magistrate and the magistrate will consider that report when making a decision. Based on your posts here you're likely to do everything you can to convince the report writer that dad is the devil. That wont work because he is not the devil...
So unless this bloke has murdered someone, has a history of child abuse or something else that relates to child abuse you're not gonna have any luck convincing the court that the bloke should not be allowed to know his own kid... IF however, tiy choose to act like a twit and insist on preventing the child knowing their dad, you are putting yourself in a position where the child could be removed from you and placed in the permenant care of the dad...
Make sure you read that last bit a few times because it is really important that you understand and realise that it is not unreasonable for a child to get to know their dad... Unless of course the dad is a child murderer, has a history of child abuse and that history is not just you saying it happened. It means police reports, charges etc etc So lets assume dad has gone to jail a few times, for drink driving, drug offenses, assault... That isn't gonna stop him seeing his kid. He needs criminal convictions for child abuse, then you're gonna be able to establish that the kid should not be allowed near dad...
Now I'm still not sure, does he just want to see his kid a few times a week? or have full custody? if he wants full custody that might be because he feels he has a good case to show that if the kid is in your care you will not provide opportunities for the kid to spend time with dad and as a result parenting arrangements need to be swapped. Now, all anyone has here is the info YOU PROVIDE and when I asked what grounds you have to establish that dad is a danger your answer was that it was non of my business... So it is pretty hard to give accurate information