  We study the stationary photon output and statistics of small lasers. Our
closed-form expressions clarify the contribution of collective effects due to
the interaction between quantum emitters. We generalize laser rate equations
and explain photon trapping: a decrease of the photon number output below the
lasing threshold, derive an expression for the stationary cavity mode
autocorrelation function $g_2$, which implies that collective effects may
strongly influence the photon statistics. We identify conditions for coherent,
thermal and superthermal radiation, the latter being a unique fingerprint for
collective emission in lasers. These generic analytical results agree with
recent experiments, complement numerical results, and provide insight into and
design rules for nanolasers.
