Stem cells, including mammalian, and particularly primate primordial stem cells (pPSCs) such as human embryonic stem cells (hESCs), hold great promise for restoring cell, tissue, and organ function. However, cultivation of stem cells, particularly undifferentiated hESCs, in serum-free, feeder-free, and conditioned-medium-free conditions remains crucial for large-scale, uniform production of pluripotent cells for cell-based therapies, as well as for controlling conditions for efficiently directing their lineage-specific differentiation. This instant invention is based on the discovery of the formulation of minimal essential components necessary for maintaining the long-term growth of pPSCs, particularly undifferentiated hESCs. Basic fibroblast growth factor (bFGF), insulin, ascorbic acid, and laminin were identified to be both sufficient and necessary for maintaining hESCs in a healthy self-renewing undifferentiated state capable of both prolonged propagation and then directed differentiation. Having discerned these minimal molecular requirements, conditions that would permit the substitution of poorly-characterized and unspecified biological additives and substrates were derived and optimized with entirely defined constituents, providing a “biologics”-free (i.e., animal-, feeder-, serum-, and conditioned-medium-free) system for the efficient long-term cultivation of pPSCs, particularly pluripotent hESCs. Such culture systems allow the derivation and large-scale production of stem cells such as pPSCs, particularly pluripotent hESCs, in optimal yet well-defined biologics-free culture conditions from which they can be efficiently directed towards a lineage-specific differentiated fate in vitro, and thus are important, for instance, in connection with clinical applications based on stem cell therapy and in drug discovery processes.