Well, I'm new but I would like to add my own theory. This explaination may make more sense than Nero being Vergil or Dante's child or some long lost brother.
We all know sometime before Devil May Cry 4, Nero had sustained an injury that had allowed a demon to infiltrate and change his right arm. And in Agnus' research facility, Nero repaired Yamato and gained a Vergil look-alike Devil Trigger in the form of a Demonic Spirit. And it was suspected that Nero had Sparda blood in him since they were able to bring the Sparda Statue to life using Nero. And it is hinted that Nero is like someone Bael (King of the Fire Hell) knew.
Vergil stayed behind in the demon world in DMC 3 but was killed by Dante in DMC 1. Maybe Demons that die just go into like a "spirit mode". So here is what I propose:
Vergil, as a spirit, returned to the Human World and infected Nero's arm with his demonic presence. This changed Nero's arm to a demonic looking thing that has the blood of Sparda inside the arm thanks to Vergil (thus giving Nero some of Vergil's character traits). Because Yamato belonged to Vergil, when Nero was in the lab, Vergil was able to repair Yamato and summon the sword to Nero's grasp. Now Vergil can achieve his Devil Trigger state at Nero's command, but since Vergil is dead, he can only appear as a Demonic Spirit rather than take on a real physical form. So I'm saying Nero isn't related to Sparda but because of Vergil's presence in his arm the blood of sparda flows through him.
May sound crazy but makes more sense to me. Please don't attack me or anything, lol.