The three main categories listed in the Baptist origins outline below are continuation, restoration, and spontaneous origination. I want to mention the last one briefly and the move on to the two main categories and their subdivisions.
Spontaneous origination has been mentioned from time to time in relation to Baptist origins. This idea, as stated by Brackney (The Baptists, p. xvii), is that "Baptists originate whenever and wherever the Holy Spirit calls forth a congregation which conforms to literal Biblical revelation, regardless of historical antecedents or relationships with other groups." Nathan Finn addresses this some on his blog . This kind of origin is "spontaneous" in that any group of people might come to the conviction that the Bible teaches the baptism of professing believers by immersion and could by that be made Baptists. Someone stated it this way: "The Baptists simply appeared and started up on their own without any succession or connection..." A down-to-earth expression of this might draw from John the Baptist's words to the Jews, "God is able of these stones to raise up Baptists."
This view should not be dismissed, for there are those that hold it. But we should recognize its basic difference from the other two views. While most views and sub-theories of Baptist origins may knit together Baptist history, Baptist identity, and Baptist polity, the spontaneous origination view does not particularly address when Baptists originated, but only how. In this sense this idea seems to be a theological construct that addresses a platform of Baptist polity -- how Baptists may come into existence (or how a church may be organized), without addressing when Baptists as we know them arose historically. This view removes itself from the idea of continuity. Both the restoration view and the continuation view agree on the existence of some kind of a historical continuity of Baptists. One believes that continuity starts at a distance from the New Testament era and the other believes that it starts from the time of Christ. According to the spontaneous view of Baptist origination, it can come at any time without any reference to any preceding group. In a sense it is "ahistorical", being unconcerned with any historical development.1
Possible implications of this view
Baptist polity -- There are no antecedents of baptism, ordination or church authority needed to form a new Baptist church.
Baptist history -- Baptist history exists whenever and wherever a group of believers form a free congregation practicing believers' immersion.
Baptist identity -- Baptist identity is solely theological, independent of any historical precedent.
With restoration, spontaneous origination shares the element that Baptists can start independently of any historical continuation or succession.
1. By this I mean the view itself. Those individuals who hold the view may be interested in Baptist history.