What would Henry VIII ask of the Anglican church once he had broken away from the Roman Catholic Church?
There are at least two ways to answer this.
On one level, all that Henry really asked of the Church of England was to grant him a divorce. The split with the Roman Catholic Church came about largely because of his desire to divorce Catherine of Aragon. When Henry split from the Church, he naturally wanted the Church of England to grant him the divorce he wanted.
On another level, we can think about what Henry wanted from the Church of England in general. What he wanted was for the church to be loyal and obedient to him. He did not have much desire to really move the Church of England away from the Catholic Church in terms of doctrine or practices. He issued things like the Six Articles, which kept celibate clergy and the doctrine of transubstantiation, among other things. These are things that were being abandoned by the Lutherans and other Protestants, but which Henry wanted to keep.
So, Henry VIII wanted his divorce, but outside of that, he did not want a radically different church. He wanted a church that would be doctrinally close to the Roman Catholic Church but which would be obedient to him.
King Henry VIII would not have formed the Anglican Church if 1) the pope had granted his request for a divorce from Catherine of Aragon and 2) if people in his court - Thomas Cromwell and his mistress/second wife Anne Boleyn - had not been persuaded him that reforming the church was in his best interest. One of the reasons that Henry VIII was open to church reform was that his treasury was depleted from building projects and wars. He took a lot of property, money, and valuable items from abbeys that he had dissolved. Another reason was that he wanted supreme loyalty from his subjects and could not stand the idea of being second to anyone, even the pope. He made all of his subjects take loyalty oaths and executed those who didn't - on the grounds of treason. The biggest factor, though, was that if he was the head of the church, he could grant himself a divorce and marry who he pleased. As he got older, he had no desire to change the basic doctrine of the church and just wanted to be the one in charge of every affair in England.