  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(Rh_(1-x)Co_x)2Si2 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 non-monotonic 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
~ 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(Rh_(1-x)Co_x)2Si2 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).
