Aims. We present the deepest and highest resolution near-infrared imaging to date of cluster Trumpler 14 in Carina. Our goal is to identify and characterise the young stellar population of this massive cluster. Methods. We made use of deep and wide-field NIR images from NTT and VLT observations, that were sensitive enough to detect substellar sources at the distance to this cluster, and at high enough resolution (VLT diffraction limited) to fully resolve the core of the cluster crowded with O stars. Results. We find that Tr14 has a well-defined core-halo structure, where less than 30% of the cluster's members reside in the core. The core is well characterised by a King function with a core radius of 0. 17 (0.14 pc at the adopted distance) and a constant baseline, the halo, of 125 sources/pc 2 . Despite the unusually large number of OB stars, the central number density at zero radius is ∼7.3 × 10 3 pc −3 , which is loose in comparison with similar clusters. We find a normal reddening law towards the cluster and derive a global reddening of A v = 2.6 ± 0.3 mag. We find convincing evidence of a sparse foreground population (∼5 sources/arcmin 2 ) reddened by about A v = 1.4 mag, which we suggest is not associated with Tr14 but is most likely an older population produced in the nearby young clusters of this complex. The colour-magnitude diagrams are compatible with ages between "zero" and ∼5 Myr, although the sources from the core of the cluster appear to concentrate on the youngest isochrones, suggesting that the halo population is, on average, slightly older than the core population. Using a set of simplistic, fixed-age, mass-luminosity relations, we derive a mass of 10 4 M for the cluster. From the NACO JHK s L data, we estimate a fraction of infrared-excess sources of 35%, although this is likely to be an underestimate given the bright completeness limits of the L band. Finally, we argue that the formerly identified proplyd candidates that fall inside our survey are not proplyds but remnants of the disrupted molecular cloud that surround the cluster. We also find a series of interesting objects in our field that are worthy of future attention: a candidate photoionised proplyd best seen in the L band, a compact nebula surrounding an early type star, and a tentative proplyd/small shock associated with a faint source.