  We consider the family of entire transcendental maps given by $F_{\lambda,m}=
\lambda z^m exp(z)$ where m>=2. All functions $F_{\lambda,m}$ have a
superattracting fixed point at z=0, and a critical point at z=-m. In the
dynamical plane we study the topology of the basin of attraction of z=0. In the
parameter plane we focus on the capture behaviour, i.e., \lambda values such
that the critical point belongs to the basin of attraction of z=0. In
particular, we find a capture zone for which this basin has a unique connected
component, whose boundary is then non-locally connected. However, there are
parameter values for which the boundary of the immediate basin of z=0 is a
quasicircle.
