Context. By studying young magnetically active late-type stars, i.e. analogues to the young Sun, we can draw conclusions on the evolution of the solar dynamo. Aims. We determine the topology of the surface magnetic field and study the relation between the magnetic field and cool photospheric spots in three young late-type stars. Methods. High-resolution spectropolarimetry of the targets was obtained with the HARPSpol instrument mounted at the ESO 3.6 m telescope. The signal-to-noise ratios of the Stokes IV measurements were boosted by combining the signal from a large number of spectroscopic absorption lines through the least squares deconvolution technique. Surface brightness and magnetic field maps were calculated using the Zeeman-Doppler imaging technique.Results. All three targets show clear signs of magnetic fields and cool spots. Only one of the targets, V1358 Ori, shows evidence of the dominance of non-axisymmetric modes. In two of the targets, the poloidal field is significantly stronger than the toroidal one, indicative of an α 2 -type dynamo, in which convective turbulence effects dominate over the weak differential rotation. In two of the cases there is a slight anti-correlation between the cool spots and the strength of the radial magnetic field. However, even in these cases the correlation is much weaker than in the case of sunspots. Conclusions. The weak correlation between the measured radial magnetic field and cool spots may indicate a more complex magnetic field structure in the spots or spot groups involving mixed magnetic polarities. Comparison with a previously published magnetic field map shows that on one of the stars, HD 29615, the underlying magnetic field changed its polarity between 2009 and 2013.