  We study the establishment of three-planet resonances -similar to the Laplace
resonance in the Galilean satellites- and their effects on the mutual
inclinations of the orbital planes of the planets, assuming that the latter
undergo migration in a gaseous disc. In particular, we examine the resonance
relations that occur, by varying the physical and initial orbital parameters of
the planets (mass, initial semi-major axis and eccentricity) as well as the
parameters of the migration forces (migration rate and eccentricity damping
rate), which are modeled here through a simplified analytic prescription. We
find that, in general, for planetary masses below 1.5 M_J, multiple-planet
resonances of the form n3:n2:n1=1:2:4 and 1:3:6 are established, as the inner
planets, m1 and m2, get trapped in a 1:2 resonance and the outer planet m3
subsequently is captured in a 1:2 or 1:3 resonance with m2. For mild
eccentricity damping, the resonance pumps the eccentricities of all planets on
a relatively short time-scale, to the point where they enter an
inclination-type resonance (as in Libert & Tsiganis 2011); then mutual
inclinations can grow to ~35{\deg}, thus forming a "3-D system". On the other
hand, we find that trapping of m2 in a 2:3 resonance with m1 occurs very
rarely, for the range of masses used here, so only two cases of capture in a
respective three-planet resonance were found. Our results suggest that trapping
in a three-planet resonance can be common in exoplanetary systems, provided
that the planets are not very massive. Inclination pumping could then occur
relatively fast, provided that eccentricity damping is not very efficient so
that at least one of the inner planets acquires an orbital eccentricity higher
than e=0.3.
