What determines the form of the intensity curves in Laser-Induced Fluorescence (LIF) measurements? What determines the form of the intensity spectra of different particle species in Laser-Induced Fluorescence (LIF) measurements? See e.g. 
I figure that bigger particles have more ways to get excited and so the intensities accumulate and make the curve wider? But how exactly do I derive an expected curve for a given molecule type? Why the steep rise and the slower fall?

 A: In short: the spectra can be explained by considering vibronic transitions, the Franck-Condon principle (http://en.wikipedia.org/wiki/Franck%E2%80%93Condon_principle), and the uncertainty principle. The explanation is as follows:
The intensity of a transition is determined by its probability amplitude $P$
\begin{equation}
P = \langle \psi ' | \hat{\mu} | \psi \rangle
\end{equation}
where $\hat{\mu}$ is the molecular dipole moment operator and $\psi$ and $\psi'$ are the wavefunctions of the initial and final states, respectively. The Franck-Condon principle tells you that electronic transitions to and from the lowest vibrational states (0-0 transitions) are most probable. These transitions are responsible for the steep rise in the signals that you mention. The "slower fall" corresponds to multiple vibronic transitions from your excited electronic state in the lowest vibrational state to excited vibrational states in a lower electronic energy level. These transitions are noticeable in fluorescence spectroscopy because, after the molecule is excited by the laser, there is enough time for some of the the energy to be dissipated as heat (i.e. rotations, translations and vibrations) before it emits a photon.  
All of these transitions are of course strictly quantized in energy and, in principle, you should be able to observe individual, discretized, lines  instead of a single broad signal. However, because of the uncertainty principle, spectral lines always show line broadening. This uncertainty (in energy units) is given approximately by
\begin{equation}
\Delta E = \hbar \tau^{-1}
\end{equation}
where $\tau$ is the lifetime of the chemical species. This lifetime can be increased by reducing the temperature and, if you take the spectra that you show above at very low temperatures, you should be able to resolve the lines of the different vibronic transitions that conform your broad signals. 
