As far as I know, other than for the GEO ring satellites are not assigned slots prior to launch.
In the United States various regulatory bodies approve the launch of Earth-orbiting satellites depending on their mission (e.g. the FCC approves frequencies and communications, NOAA approves Earth-imaging satellites, etc.). Part of this licensing process typically includes an analysis that shows the 25-year on-orbit requirement will be met. As of 2008, this includes what's known as a conjunction analysis, which looks at the probability of the new spacecraft intersecting old ones.
So the short answer is that slots are not assigned, but (at least in the US) analysis is required to show the spacecraft has a low probability of hitting something already in orbit.
Unfortunately in practice conjunction analysis is very computationally expensive and requires government assistance (as the orbits of many national security assets are not published). Also, because of the uncertainty in ephemerides and other perturbations that build-up on orbit, it's not a good prediction of the probability of collision on a timescale anywhere close to 25 years. That's why despite this type of analysis things still collide.