Perturbative analysis of parton kinetics for high energy nuclear collisions shows that thermal equilibration of gluons happens very fast, while quark production is much slower. A simple "minimal model" is proposed which includes only incoming quarks and antiquarks. We have found that a smaller quark number is more than compensated by the fact that they are imbedded into the hotter glue. Predicted yield of dileptons and photons in the interesting kinematic region are larger than considered before, and are quite observable at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider. PACS numbers: 25.75.+r, 12.38.Mh, 24.85.+p The main objective of the future experimental heavyion program at the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC) is the production and studies of a new form of matter, the so-called quark-gluon plasma (QGP) [1], which is expected to exist during the first few fm/c of the collisions. Extrapolations from lower energies are difficult, because for heavy ion collisions at RHIC and LHC energies one is entering a new dynamical regime, in which the so-called semihard processes, involving partons with momenta (and momenta transfer) p ~l-3 GeV, can no longer be considered as isolated rare events, but are involved in some complicated, cascade-type processes.Early discussions of parton kinetics taking place after the primary collisions can be found in [1], and that of "partonic saturation" effects occurring before the collision can be found in [2]. The role of few-GeV partons (known also as "mini-jets") in nuclear collisions was discussed in [3][4][5]. Among important recent developments are estimates of parton energy losses in QGP (see [6] and references therein), which for the gluons reach TgdE/dx «2-3 GeV/fm. Thus, contrary to some earlier claims, most of the mini-jets should be trapped in the fireball, created in central collisions, and therefore contribute to equilibration processes.One open question is whether the main amount of produced entropy is due to complicated partonic substructure of nuclei themselves, and this entropy is just "liberated" at the collision moment, or it is produced in a more conventional manner, due to rescattering and production processes after the primary collisions took place. Assuming that perturbative QCD and parton model to be applicable down to 1 GeV scale (x ~0.01, at RHIC), one may come to the former conclusion [5]. If gluonic structure functions are indeed so "dense," that one can speak about QGP as soon as partons are separated from each other after the first collision, at the time scale ^separation ~ 1/pt ~ 0.2 fm/c. Consequences of this (the most optimistic) scenario for dileptons were recently discussed in [7]; it leads to very high initial temperatures and very big yields. However, we do not think such a regime can be dynamically sustained (at least, not if one is using perturbative cross sections).The specific "hot-glue" scenario to be discussed below was recently suggested by one of us [8]. An amb...