Motivated by recent observational and numerical studies suggesting that collapsing protostellar cores may be replenished from the local environment, we explore the evolution of protostellar cores submerged in the external counter-rotating environment. These models predict the formation of counter-rotating disks with a deep gap in the gas surface density separating the inner disk (corotating with the star) and the outer counter-rotating disk. The properties of these gaps are compared to those of planet-bearing gaps that form in disks hosting giant planets. We employ numerical hydrodynamics simulations of collapsing cores that are replenished from the local counter-rotating environment, as well as numerical hydrodynamic simulations of isolated disks hosting giant planets, to derive the properties of the gaps that form in both cases. Our numerical simulations demonstrate that counter-rotating disks can form for a wide range of mass and angular momentum available in the local environment. The gap that separates both disks has a depletion factor smaller than 1%, can be located at a distance from ten to over a hundred AU from the star, and can propagate inward with velocity ranging from 1 AU/Myr to >100 AU/Myr. Unlike our previous conclusion, the gap can therefore be a long-lived phenomenon, comparable in some cases to the lifetime of the disk itself. For a proper choice of the planetary mass, the viscous alpha-parameter and the disk mass, the planet-bearing gaps and the gaps in counter-rotating disks may show a remarkable similarity in the gas density profile and depletion factor, which may complicate their observational differentiation.
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