Supermassive black holes with billion solar masses are in place already within the first Gyr, however, their origin and growth in such a short lapse of time is extremely challenging to understand. Here, we discuss the formation paths of early black-hole seeds, showing the limits of light black-hole seeds from stellar origin and the expected characteristics of heavy/massive black-hole seeds originated by gas direct collapse in peculiar primordial conditions. To draw conclusions on the possible candidates and the role of the ambient medium, we use results from N-body hydrodynamic simulations including atomic and molecular non-equilibrium abundance calculations, cooling, star formation, feedback mechanisms, stellar evolution, metal spreading of several heavy elements from SNII, AGB and SNIa, and multifrequency radiative transfer over 150 frequencies coupled to chemistry and SED emission for popII-I and popIII stellar sources. Standard stellar-origin light black holes are unlikely to be reliable seeds of early supermassive black holes, because, under realistic assumptions, they cannot grow significantly in less than a billion years. Alternatively, massive black-hole seeds might originate from direct collapse of pristine gas in primordial quiescent mini-haloes that are exposed to stellar radiation from nearby star forming regions. The necessary conditions required to form these heavy seeds must be complemented with information on the complex features of local environments and the fine balance between chemistry evolution and radiative transfer.