Abstract The theory of free clusters in thin soft magnetic layers has been further developed by investigating their conversions. A wall cluster is a collection of domain walls (considered to be infinitely thin surfaces over which the magnetization abruptly changes its direction) that have one intersection line, the so-called cluster knot, in common. The cluster knot of a free wall cluster does not coincide with any of the bounding edges of the magnetic geometry. The domain structure is considered as a concatenation of wall clusters, in which already existing clusters initiate the development of new ones, which subsequently provide for an extension in the domain structure. Only reversible changes in the domain structure are considered. In this context, the fact that the creation line is the orthogonal trajectory to a continuous magnetization field plays a crucial role in the creation of (sub)clusters. This takes place without having to overcome a threshold formed by the domain-wall energy. Concave and convex subclusters are defined in order to facilitate the analysis of the creation of new (sub)clusters. It is shown, among other things, that a concave subcluster consists of an even number of uniform domains. The part that these types of subclusters play in free-cluster conversions is demonstrated. Bifurcation of clusters has been considered in detail, and the boundaries of the sectors, in which the intermediate domain wall between both clusters has to be situated, are given. The theoretical findings are supported by experimental evidence.