We present a study of the evolution of magnetism from the quantum critical system YbRh2Si2 to the stable trivalent Yb system YbCo2Si2. Single crystals of Yb(Rh1-x Co-x)(2)Si-2 were grown for 0 <= x <= 1 and studied by means of magnetic susceptibility, electrical resistivity, and specific heat measurements, as well as photoemission spectroscopy. The results evidence a complex magnetic phase diagram, with a nonmonotonic evolution of T-N and two successive transitions for some compositions resulting in two tricritical points. The strong similarity with the phase diagram of YbRh2Si2 under pressure indicates that Co substitution basically corresponds to the application of positive chemical pressure. Analysis of the data proves a strong reduction of the Kondo temperature T-K with increasing Co content, T-K becoming smaller than T-N for x approximate to 0.5, implying a strong localization of the 4f electrons. Furthermore, low-temperature susceptibility data confirm a competition between ferromagnetic and antiferromagnetic exchange. The series Yb(Rh1-xCox)(2)Si-2 provides an excellent experimental opportunity to gain a deeper understanding of the magnetism at the quantum critical point in the vicinity of YbRh2Si2 where the antiferromagnetic phase disappears (T-N -> 0).