  Context. The origin of the fossil magnetic fields detected in 5 to 10% of
intermediate-mass main sequence stars is still highly debated. Aims. We want to
bring observational constraints to a large population of intermediate-mass
pre-main sequence (PMS) stars in order to test the theory that
convective-dynamo fields generated during the PMS phases of stellar evolution
can occasionally relax into fossil fields on the main sequence. Methods. Using
distance estimations, photometric measurements, and spectropolarimetric data
from HARPSpol and ESPaDOnS of 38 intermediate-mass PMS stars, we determined
fundamental stellar parameters (Teff, L and v sin i) and measured surface
magnetic field characteristics (including detection limits for non-detections,
and longitudinal fields and basic topologies for positive detections). Using
PMS evolutionary models, we determined the mass, radius, and internal structure
of these stars. We compared different PMS models to check that our
determinations were not model-dependant. We then compared the magnetic
characteristics of our sample accounting for their stellar parameters and
internal structures. Results. We detect magnetic fields in about half of our
sample. About 90% of the magnetic stars have outer convective envelopes larger
than ~25% of the stellar radii, and heavier than ~2% of the stellar mass. Going
to higher mass, we find that the magnetic incidence in intermediate-mass stars
drops very quickly, within a time-scale of the order of few times 0.1 Myr.
Finally, we propose that intermediate-mass T Tauri stars with large convective
envelopes, close to the fully convective limit, have complex fields and that
their dipole component strengths may decrease as the sizes of their convective
envelopes decrease, similar to lower-mass T Tauri stars.
