  Let $L_H$ denote the set of all normalized locally one-to-one and
sense-preserving harmonic functions in the unit disc $\Delta$. It is well-known
that every complex-valued harmonic function in the unit disc $\Delta$ can be
uniquely represented as $f = h + \overline{g}$, where $h$ and $g$ are analytic
in $\Delta$. In particular the decomposition formula holds true for functions
of the class $L_H$. For a fixed analytic function $h$, an interesting problem
arises - to describe all functions $g$, such that $f$ belongs to $L_H$.
  The case when $f\in L_H$ and $h$ is the identity mapping was considered [2].
More general results are given in [3], where $f\in L_H$ and letting $h$ to be a
convex analytic mapping. The focus of our present research is to characterize
the set of all functions $f\in L_H$ having starlike analytic part $h$. In this
paper, we provide coefficient, distortion and growth estimates of $g$. We also
give growth and Jacobian estimates of $f$.
