Quantum vortices in superfluids may capture matter and deposit it inside their core. By doping vortices with foreign particles one can effectively visualize them and study them experimentally. To acquire a better understanding of the interaction between quantum vortices and matter, and clarify the details of recent experiments, the properties of doped vortices are investigated here theoretically in the regimes where the doping mass becomes close to the total mass of superfluid particles forming a vortex. Such formations are dynamically stable and, possessing both vorticity and enhanced inertia, demonstrate properties that are different from the pure vortex case. The goal of this paper is to define and investigate the universal aspects of heavily doped vortex behavior, which can be realized in different types of quantum mixtures. The proposed 3D model is based on a system of coupled semiclassical matter wave equations that are solved numerically in a wide range of physical parameters. The size, geometry and binding energy of dopants in different regimes are discussed. The coupled motion of a vortex-dopant complex and decoupling conditions are studied. The reconnection of vortices, taken as an example of a fundamental process responsible for the evolution of a quantum turbulent state, is modeled to illustrate the difference between the light and heavy doping cases.Illuminating experiments in quantum turbulence were performed recently using superfluid helium nanodroplets [13][14][15][16]. Vortex filaments in rotating droplets were doped with Ag and Xe atoms and studied using a femtosecond x-ray coherent diffractive imaging technique as well as electron microscopy preceded by surfacedeposition of the samples. Several questions were raised in these works, including the origin of unusual shapes of doped helium droplets and distribution of vortices inside the droplet. Although certain aspects were clarified by theorists [17][18][19], the connection between the rotational motion of a droplet and a dopant still remains unclear [16]. In nanodroplet experiments doping particles are approximately 33 times heavier than fluid atoms and the diameter of each particle is comparable with a vortex core size in helium. This is quite opposite, for instance, in comparison to large and light electron bubbles often used as dopants and well studied in the past both experimentally and theoretically [20][21][22]. Being captured, heavy particles may influence the vortex motion significantly and theoretical modeling is necessary to understand the details of their behavior.According to the results of Gordon and colleagues [8,9], guest atoms in helium above a critical temperature tend to form spherical clusters. In superfluid helium below critical temperature impurities with a certain probability stick together to produce long cylindrical filaments, which are attributed to the presence of quantum vortices. These filaments are stable enough to exist independently, by decoupling from vortices, which allows them to be studied using a surface-depo...