The static dipole polarizabilities of the group 13 elements Ga, In and Tl in the three P-2(JMJ) substates are calculated by the Fock space coupled cluster method. The ground P-2(1/2) states are also studied by the single reference coupled cluster approach, with triple excitations included perturbatively. Very large basis sets are employed and extended to convergence. The effects of different parameters in the calculation (2-vs. 4-component Hamiltonian, basis sets, coupled cluster expansion) are explored. The effect of the Gaunt interaction, which approximates the lowest order relativistic correction to the two-electron interaction, is also studied. Error bounds are estimated at 3% for the ground states and 5% for the J = 3/2 states. The final recommended values for the ground states are alpha(Ga) = 51.1(1.5) a.u., alpha(In) = 62.0(1.9) a.u., and alpha(Tl) = 52.1(1.6) a.u. The last two are in agreement with the experimental alpha(In) = 69(8) a.u. and alpha(Tl) = 51(7) a.u., and have error bars 4 times smaller. No experimental value is available for Ga, and the present calculations provide the first error bars for this element. (C) 2011 Elsevier B.V. All rights reserved.