  Radio galaxies with jets of relativistic particles are usually hosted by
massive elliptical galaxies with active nuclei powered by accretion of
interstellar matter onto a supermassive black hole. In some rare cases (<5%),
their jets drive the overall structure to sizes larger than 700 kpc, and they
are called giant radio galaxies (GRGs). A very small fraction of the population
of such radio galaxies contains molecular and atomic gas in the form of rings
or discs that can fuel star formation. The origin of this gas is not well
known; it has sometimes been associated with a minor merger with a gas-rich
disc galaxy (e.g. Centaurus A) or cooling of material from a hot X-ray
atmosphere (e.g. cooling flows). The giant radio jets might be the extreme
evolution of these objects, and they can teach us about the radio galaxy
evolution. We selected 12 targets from a catalogue of 820 GRGs that are likely
to be in a gas-accretion and star formation phase. The targets were selected
from the mid-infrared to contain heated dust. We report here the results of
IRAM-30m observations, the molecular gas content, and the star formation
efficiency, and we discuss the origin of the gas and disc morphology. Three out
of our 12 targets are detected, and for the others, we report significant upper
limits. We combine our three detections and upper limits with four additional
detected GRGs from the literature to discuss the results. Most of the GRG
targets belong to the main sequence, and a large fraction are in the passive
domain. Their star formation efficiency is comparable to normal galaxies,
except for two galaxies that are deficient in molecular gas with a short
(~200Myr) depletion time, and a quiescent gas-rich giant spiral galaxy. In
general, the depletion time is much longer than the lifetime of the giant radio
jet.
