  Extending previous work [T. Pusztai, L. R\'atkai, A. Sz\'all\'as, and L.
Gr\'an\'asy, Phys. Rev. E {\bf 87}, 032402 (2013)], we have studied the
formation of eutectic dendrites in a model ternary system within the framework
of the phase-field theory. We have mapped out the domain in which two-phase
dendritic structures grow. With increasing pulling velocity, the following
sequence of growth morphologies is observed: flat front lamellae $\rightarrow$
eutectic colonies $\rightarrow$ eutectic dendrites $\rightarrow$ dendrites with
target pattern $\rightarrow$ partitionless dendrites $\rightarrow$
partitionless flat front. We confirm that the two-phase and one-phase dendrites
have similar forms, and display a similar scaling of the dendrite tip radius
with the interface free energy. It is also found that the possible eutectic
patterns include the target pattern, and single- and multiarm spirals, of which
the thermal fluctuations choose. The most probable number of spiral arms
increases with increasing tip radius and with decreasing kinetic anisotropy.
Our numerical simulations confirm that in agreement with the assumptions of a
recent analysis of two-phase dendrites [S. Akamatsu, S. Bottin-Rousseau, G.
Faivre, and E. A. Brener, Phys. Rev. Lett. {\bf 112}, 105502 (2014)], the
Jackson-Hunt scaling of the eutectic wavelength with pulling velocity is obeyed
in the parameter domain explored, and that the natural eutectic wavelength is
proportional to the tip radius of the two-phase dendrites. Finally, we find
that it is very difficult/virtually impossible to form spiraling two-phase
dendrites without anisotropy, an observation that seems to contradict the
expectations of Akamatsu {\it et al.}. Yet, it cannot be excluded, that in
isotropic systems two-phase dendrites are rare events difficult to observe in
simulations.
