Context : Aims : We study the origin of tail-like structures recently detected around the disk of SU Aurigae and several FU Orionis type stars . Methods : Dynamic protostellar disks featuring ejections of gaseous clumps and quiescent protoplanetary disks experiencing a close encounter with an intruder star were modelled using the numerical hydrodynamics code FEOSAD . Both the gas and dust dynamics were taken into account , including dust growth and mutual friction between the gas and dust components . Only plane-of-the-disk encounters were considered . Results : Ejected clumps produce a unique type of tails that are characterized by a bow-shock shape . These tails owe its origin to the supersonic motion of the ejected clumps through the dense envelope , which often surrounds young gravitationally unstable protostellar disks . The ejected clumps either sit at the head of the tail-like structure or disperse if their mass is insufficient to withstand the head wind of the envelope . On the other hand , close encounters with quiescent protoplanetary disks produce three types of the tail-like structures , which we defined as pre-collisional , post-collisional , and spiral tails . These tails can in principle be distinguished by peculiar features of the gas and dust flow in and around them . We found that the brown-dwarf-mass intruders do not capture circumintruder disks during the encounter , while the sub-solar-mass intruders can acquire appreciable circumintruder disks with elevated dust-to-gas ratios , which can ease their observational detection . However , this is true only for prograde collisions ; the retrograde intruders fail to collect an appreciable gas and dust from the disk of the target . The masses of gas in the tails vary in the 0.85–11.8 M _ { Jup } limits , while the total mass of dust lies in the 1.75–30.1 M _ { \oplus } range , with the spiral tails featuring the highest masses . The predicted mass of dust in the model tail-like structures is therefore higher than what was inferred for similar structures in SU Aur , FU Ori , and Z CMa , making their observational detection feasible . Conclusions : Tail-like structures around protostellar and protoplanetary disks can act as a smoking gun to infer interesting phenomena , such as clump ejection or close encounters . particular , the bow-shock morphology of the tails could point to clump ejections as a possible formation mechanism . Further numerical and observational studies are needed to better understand the detectability and properties of the tails .