Linearly invariant families of harmonic locally quasiconformal mappings

In [2,3] harmonic locally $K$-quasiconformal families of functions de ned in the unit disc were introduced. In this paper we continue the study of the boundary behaviour of maps form such families. In particular, for functions $f$ from the family we investigate cluster sets $C(e^{i\theta}, f)$ and consider the problem od degenerating of a cluster set to a point.