We perform a comparative numerical hydrodynamics study of embedded protostellar disks formed as a result of the gravitational collapse of cloud cores of distinct mass (M_cl=0.2--1.7 M_sun) and ratio of rotational to gravitational energy (beta=0.0028--0.023). An increase in M_cl and/or beta leads to the formation of protostellar disks that are more susceptible to gravitational instability. Disk fragmentation occurs in most models but its effect is often limited to the very early stage, with the fragments being either dispersed or driven onto the forming star during tens of orbital periods. Only cloud cores with high enough M_cl or beta may eventually form wide-separation binary/multiple systems with low mass ratios and brown dwarf or sub-solar mass companions. It is feasible that such systems may eventually break up, giving birth to rogue brown dwarfs. Protostellar disks of {it equal} age formed from cloud cores of greater mass (but equal beta) are generally denser, hotter, larger, and more massive. On the other hand, protostellar disks formed from cloud cores of higher beta (but equal M_cl) are generally thinner and colder but larger and more massive. In all models, the difference between the irradiation temperature and midplane temperature triangle T is small, except for the innermost regions of young disks, dense fragments, and disks outer edge where triangle T is negative and may reach a factor of two or even more. Gravitationally unstable, embedded disks show radial pulsations, the amplitude of which increases along the line of increasing M_cl and beta but tends to diminish as the envelope clears. We find that single stars with a disk-to-star mass ratio of order unity can be formed only from high-beta cloud cores, but such massive disks are unstable and quickly fragment into binary/multiple systems.
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