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We present a semi-analytical population synthesis model of protoplanetaryclumps formed by disk instability at radial distances of 80 - 120 AU. Variousclump density profiles, initial mass functions, protoplanetary disk models,stellar masses, and gap opening criteria are considered. When we use morerealistic gap opening criteria, we find that gaps open only rarely whichstrongly affects clump survival rates and their physical properties (mass,radius and radial distance). The inferred surviving population is then shiftedtowards less massive clumps at smaller radial distances. We also find thatpopulations of surviving clumps are very sensitive to the model assumptions andused parameters. Depending on the chosen parameters, the protoplanets occupy amass range between 0.01 and 16 $M_{\text{J}}$ and may either orbit close to thecentral star or as far out as 75 AU, with a sweet spot at 10-30 AU for themassive ones. However, in all the cases we consider we find that massive giantplanets at very large radial distances are rare in qualitative agreement withcurrent direct imaging surveys. We conclude that caution should be taken inderiving population synthesis models as well as when comparing the models'results with observations.

On the diversity in mass and orbital radius of giant planets formed via disk instability