Anglicanism is a tradition within Christianity comprising churches with historical connections to the Church of England or similar beliefs, worship and church structures. The word Anglican originates in ecclesia anglicana, a medieval Latin phrase dating to at least 1246 that means the English Church. Adherents of Anglicanism are called Anglicans. The great majority of Anglicans are members of churches which are part of the international Anglican Communion.
Following the American Revolution, Anglican congregations in the United States and Canada were each reconstituted into autonomous churches with their own bishops and self-governing structures. This was adopted as the model for many newly formed churches. Today, all 38 member churches of the Anglican Communion are fully autonomous, each with its own primate and governing structure. Not all member churches of the Anglican Communion use the word "Anglican" in their name. For example, the mainline Anglican church in the United States is called the Episcopal Church, and its members are referred to as Episcopalians.
When Grantville arrived in 1631, Anglicanism was the Church of England (established in England and Wales), and the Church of Ireland. Except for England's few overseas colonies, it had not expanded beyond the British Isles, and even there, it was only predominant in England and Wales. While the Church of Ireland was established, the people of Ireland were predominantly Catholic.
When the Ring of Fire fell in 2000, Grantville's Episcopal church, which dated to 1897, was closed and dilapidated. After the RoF, the town's handful of Episcopalians used lay readers and prayer services, while Veleda Riddle relentlessly petitioned the Archbishop of Canterbury, William Laud, to appoint a bishop for Grantville, or at least send a priest there. She also began a campaign to restore the church building. By 1635, the building was usable, though not fully restored. In February of 1635, Robert Herrick arrived for a six-month stint as minister, but he only accepted the position so he could have room and board while he used the town's libraries. In August, Herrick left, and was replaced by William Barneby.
In February of 1634, Laud was arrested and thrown into the Tower of London. In May of that year, he was one of the people rescued by Harry Lefferts' commando team, and was taken to the Netherlands. There, he set up an archbishopric-in-exile, and apparently got some assistance from Thomas Wentworth.
By August of 1635, between up-time Episcopalians leaving Grantville, English ex-mercenaries settling in the United States of Europe, and people who had fled Charles I's England, there was a small-scale Anglican diaspora in the USE. This let Archbishop Laud justify naming Robert Herrick as the Anglican bishop for the USE, with his seat at Magdeburg.
The future of Anglicanism in the 1632 timeline is still unclear. For one thing, not much has been written about it. There has apparently been no mention of Laud being replaced in Canterbury, or of who his replacement, if there is one, is. Robert Herrick has only appeared in one story, though he was briefly mentioned in another as being on his way to Grantville. It is not yet clear what kind of bishop he will be, or how well he will do. It is also not clear how, or how well, either Laud or Herrick will eventually deal with the differences between up-time American Episcopalianism and down-time Anglicanism, especially with regard to issues such as the role of women in the church.