  We performed a deep wide-field (6.76 deg^2) near-infrared survey with the
VISTA telescope that covers the entire extent of the Carina nebula complex
(CNC). The point-source catalog created from these data contains around four
million individual objects down to masses of 0.1 M_sun. We present a
statistical study of the large-scale spatial distribution and an investigation
of the clustering properties of infrared-excesses objects, which are used to
trace disk-bearing young stellar objects (YSOs). We find that a (J - H) versus
(Ks - [4.5]) color-color diagram is well suited to tracing the population of
YSO-candidates (cYSOs) by their infrared excess. We identify 8781 sources with
strong infrared excess, which we consider as cYSOs. This sample is used to
investigate the spatial distribution of the cYSOs with a nearest-neighbor
analysis. The surface density distribution of cYSOs agrees well with the shape
of the clouds as seen in our Herschel far-infrared survey. The strong decline
in the surface density of excess sources outside the area of the clouds
supports the hypothesis that our excess-selected sample consists predominantly
of cYSOs with a low level of background contamination. This analysis allows us
to identify 14 groups of cYSOs outside the central area. Our results suggest
that the total population of cYSOs in the CNC comprises about 164000 objects,
with a substantial fraction (~35%) located in the northern, still not well
studied parts. Our cluster analysis suggests that roughly half of the cYSOs
constitute a non-clustered, dispersed population.
