Weak decays in heavy nuclei with charge numbers Z = 101 − 109 are studied within a microscopic formalism based on deformed self-consistent Skyrme Hartree-Fock mean-field calculations with pairing correlations. The half-lives of β + decay and electron capture are compared with αdecay half-lives obtained from phenomenological formulas. Transfermium isotopes of Md, No, Lr, Rf, Db, Sg, Bh, Hs, and Mt that can be produced in the frontier of cold and hot fusion-evaporation channels are considered. Several isotopes are identified whose β + /EC-and α-decay half-lives are comparable. The competition between these decay modes opens the possibility of new pathways towards the islands of stability.