Generation and propagation of fast electrons in laser targets consisting of thin nanofilaments are studied numerically and analytically. Such targets completely absorb laser radiation and exhibit a large coefficient of laser-energy conversion to kinetic energy of a flow of fast electrons. Analytical estimates show that the optimal thickness of the filament is on the order of the skin depth of the laser plasma, while an optimal distance between filaments is on the order of the Debye radius of hot electrons. A bunch of relativistic electrons can propagate as far as several hundred micrometers in such targets, while the fastest electrons can propagate several millimeters. Upon bending of filaments, the flow of electrons propagates along the filaments and can be focused by bringing the filaments together. Laser targets of the discussed composition are used as sources of dense bunches of relativistic electrons and subsequent generation of high-intensity X-ray radiation with their help.