  We present the statistical analysis of a subsample of 45 young stars
surrounded by protoplanetary disks (PPDs). This is the largest imaging survey
uniquely focused on PPDs to date. Our goal is to search for young forming
companions embedded in the disk material and to constrain their occurrence rate
in relation to the formation mechanism. We used principal component analysis
based point spread function subtraction techniques to reveal young companions
forming in the disks. We calculated detection limits for our datasets and
adopted a black-body model to derive temperature upper limits of potential
forming planets. We then used Monte Carlo simulations to constrain the
population of forming gas giant companions and compare our results to different
types of formation scenarios. Our data revealed a new binary system (HD38120)
and a recently identified triple system with a brown dwarf companion orbiting a
binary system (HD101412), in addition to 12 known companions. Furthermore, we
detected signals from 17 disks, two of which (HD72106 and TCrA) were imaged for
the first time. We reached median detection limits of L =15.4 mag at 2.0
arcsec, which were used to investigate the temperature of potentially embedded
forming companions. We can constrain the occurrence of forming planets with
semi-major axis a in [20 - 500] au and Teff in [600 - 3000] K, in line with the
statistical results obtained for more evolved systems from other direct imaging
surveys. The NaCo-ISPY data confirm that massive bright planets accreting at
high rates are rare. More powerful instruments with better sensitivity in the
near- to mid-infrared are likely required to unveil the wealth of forming
planets sculpting the observed disk substructures.
