  We investigate the Hubbard model on the anisotropic triangular lattice with
two hopping parameters $t$ and $t^\prime$ in different spatial directions,
interpolating between decoupled chains ($t=0$) and the isotropic triangular
lattice ($t=t^\prime$). Variational wave functions that include both Jastrow
and backflow terms are used to compare spin-liquid and magnetic phases with
different pitch vectors describing both collinear and coplanar (spiral) order.
For relatively large values of the on-site interaction $U/t^\prime \gtrsim 10$
and substantial frustration, i.e., $0.3\lesssim t/t^\prime \lesssim 0.8$, the
spin-liquid state is clearly favored over magnetic states. Spiral magnetic
order is only stable in the vicinity of the isotropic point, while collinear
order is obtained in a wide range of inter-chain hoppings from small to
intermediate frustration.
