The island-size distribution scaling function f
i (u) corresponding to submonolayer epitaxial growth with critical island size i is studied via kinetic Monte Carlo simulations for i = 0, 1, 2, and 3. An analytic form for f
i (u) based on a conjecture for the small-u behavior is also presented. For i = 1, the scaled island-size distribution is found to depend on island morphology. In particular, for fractal islands with i = 1 there is excellent agreement with our analytical form as well as with experiments on low temperature Fe/Fe(100) deposition. However, for compact islands with i = 1, the scaled distribution is found to deviate slightly at small u. We also find excellent agreement between our analytical form, simulations, and experiment for i =- 2 and i = 3. Good agreement between our simulation results for i = 0 and recent experiments on Fe/Cu(100) deposition is also found. Results for the scaling of the island-density as well as crossover scaling forms for the transition from i = 1 to i = 2 and from i = 1 to i = 3 are also presented and used to determine the one-bond activation energy and critical island size transition temperature for Fe/Fe(100). The morphology of fractal islands for i = 2 is also studied and compared with experiments on Au/Ru(0001).