"There is lot of confusion regarding Anulom marriage . Some say it is allowed and varna of the child is Varna of the father"
The varna of the child remains as of father if
- father first marry in his own varna (else father himself lost his varna) ["Prince Nabhag (son of King Dishta) married a girl from vaisya family without first marrying within his own kshatriya varna. Thus he was declared a vaisya." ~ Can a Kshatriya man marry Vaishya woman?]
- and the mother is from the same or immediate next below varna
- son of Brahmana man and Brahmana or Kshatriya woman -> Brahmana
- son of Kshatriya man and Kshatriya or Vaisya woman -> Kshatriya
- son of Vaisya man and Vaisya or Sudra woman -> Vaisya
- son of Sudra man and Sudra woman -> Sudra
"Bhishma said, 'In the beginning, the Lord of all creatures created the four orders and laid down their respective acts or duties, for the sake of sacrifice.
The Brahmana may take four wives, one from each of the four orders. In two of them (viz., the wife taken from his own order and that taken from the one next below), he takes birth himself (the children begotten upon them being regarded as invested with the same status as his own). Those sons, however, that are begotten by him on the two spouses that belong to the next two orders (viz., Vaisya and Sudra), are inferior, their status being determined not by that of their father but by that of their mothers. The son that is begotten by a Brahmana upon a Sudra wife is called Parasara, implying one born of a corpse, for the Sudra woman's body is as inauspicious as a corpse. He should serve the persons of his (father's) race. Indeed, it is not proper for him to give up the duty of service that has been laid down for him. Adopting all means in his power, he should uphold the burden of his family. Even if he happens to be elder in age, he should still dutifully serve the other children of his father who may be younger to him in years, and bestow upon them whatever he may succeed in earning.
A Kshatriya may take three wives. In two of them (viz., the one taken from his own order and the other that is taken from the order immediately below), he takes birth himself (so that those children are invested with the status of his own order). His third wife being of the Sudra order is regarded as very inferior. The son that he begets upon her comes to be called as an Ugra.
The Vaisya may take two spouses. In both of them (viz., the one taken from his own order, and the other from the lowest of the four pure orders), he takes birth himself (so that those children become invested with the status of his own order).
The Sudra can take only one wife, viz., she that is taken from his own order. The son begotten by him upon her becomes a Sudra. ~Mahabharata: Anusasana Parva
"What will be the Varna of a child born from a Brahmin man and Shudra woman?"
As per above Mahabharata text, the son that is begotten by a Brahmana upon a Sudra wife is called Parasara, his duties are to serve his father's race.