We argue that the toroidal fields developing in a magnetically accelerated jet are sufficiently unstable that they cannot contribute much to collimation. We show how an initially collimated jet is decollimated by decay of the toroidal field and by the build-up of internal pressure due to kink instability. We propose that most of the collimation of observed jets is due to the poloidal field anchored in the disc. We show how the collimation by this mechanism depends on the distribution of poloidal field strength in the disc. We find that the maximum achievable collimation increases with the ratio of outer to inner disc radius, and can be of the order of 1 deg. This dependence is found to be consistent with the available data, in particular the absence of collimated outflows from cataclysmic variables. Because of the decay of the toroidal field a new characteristic distance plays a role: the collimation distance, z_c, of the order of the disc radius or less. Beyond z_c the jet is entirely ballistic and only weakly magnetic. No external medium is needed beyond this distance to explain observed narrow opening angles of jets, and no interaction with an external medium is necessary to explain the parallel field orientation observed in fast jets.