We present a CO ( 1-0 ) survey for cold molecular gas in a representative sample of 13 high- z radio galaxies ( HzRGs ) at 1.4 < z < 2.8 , using the Australia Telescope Compact Array . We detect CO ( 1-0 ) emission associated with five sources : MRC 0114-211 , MRC 0152-209 , MRC 0156-252 , MRC 1138-262 and MRC 2048-272 . The CO ( 1-0 ) luminosities are in the range L ^ { \prime } _ { CO } \sim ( 5 - 9 ) \times 10 ^ { 10 } K km s ^ { -1 } pc ^ { 2 } . For MRC 0152-209 and MRC 1138-262 part of the CO ( 1-0 ) emission coincides with the radio galaxy , while part is spread on scales of tens of kpc and likely associated with galaxy mergers . The molecular gas mass derived for these two systems is { M } _ { H 2 } \sim 6 \times 10 ^ { 10 } { M } _ { \odot } ( M _ { H 2 } / L ^ { \prime } _ { CO } = 0.8 ) . For the remaining three CO-detected sources , the CO ( 1-0 ) emission is located in the halo ( \sim 50-kpc ) environment . These three HzRGs are among the fainter far-IR emitters in our sample , suggesting that similar reservoirs of cold molecular halo gas may have been missed in earlier studies due to pre-selection of IR-bright sources . In all three cases the CO ( 1-0 ) is aligned along the radio axis and found beyond the brightest radio hot-spot , in a region devoid of 4.5 \mu m emission in Spitzer imaging . The CO ( 1-0 ) profiles are broad , with velocity widths of \sim 1000 - 3600 km s ^ { -1 } . We discuss several possible scenarios to explain these halo reservoirs of CO ( 1-0 ) . Following these results , we complement our CO ( 1-0 ) study with detections of extended CO from the literature and find at marginal statistical significance ( 95 \% level ) that CO in HzRGs is preferentially aligned towards the radio jet axis . For the eight sources in which we do not detect CO ( 1-0 ) , we set realistic upper limits of L ^ { \prime } _ { CO } \sim 3 - 4 \times 10 ^ { 10 } K km s ^ { -1 } pc ^ { 2 } . Our survey reveals a CO ( 1-0 ) detection rate of 38 \% , allowing us to compare the CO ( 1-0 ) content of HzRGs with that of other types of high- z galaxies .