I start by a quote and definition from Roland Allen on the term “Spontaneous Expansion”.
‘What do I mean by “spontaneous expansion”? I mean the expansion which follows activity of individual members of the Church explaining to others the Gospel which they have found for themselves. It is the expansion which follows the irresistible attraction of the Christian Church for men and women who see its ordered life, and are drawn to it by desire to discover the secret of a life which they instinctively desire to share with others. I mean also the expansion of the Church by the addition (planting) of new churches.’
Roland Allen, The Spontaneous Expansion of the Church: And the Causes Which Hinder It, American ed.
(Grand Rapids, MI: Wm. B. Eerdmans Publishing Company, 1962), page 7.
Quotations that I give will be more of a ‘paraphrase’ than a direct quote for readability and understanding.