Asteroid families that are less than one million years old offer a unique possibility to investigate recent asteroid disruption events and test ideas about their dynamical evolution. Observations provided by powerful all-sky surveys have led to an enormous increase in the number of detected asteroids over the past decade. When the known populations are well characterized, they can be used to determine asteroid detection probabilities, including those in young families, as a function of their absolute magnitude. We use observations from the Catalina Sky Survey (CSS) to determine the bias-corrected population of small members in four young families down to sizes equivalent to several hundred meters. Using the most recent catalog of known asteroids, we identified members from four young families for which the population has grown appreciably over recent times. A large fraction of these bodies have also been detected by CSS. We used synthetic populations of asteroids, with their magnitude distribution controlled by a small number of parameters, as a template for the bias-corrected model of these families. Applying the known detection probability of the CSS observations, we could adjust these model parameters to match the observed (biased) populations in the young families. In the case of three families, Datura, Adelaide, and Rampo, we find evidence that the magnitude distribution transitions from steep to shallow slopes near 300 to 400 meters. Conversely, the Hobson family population may be represented by a single power-law model. The Lucascavin family has a limited population; no new members have been discovered over the past two decades. We consider a model of parent body rotational fission with the escaping secondary tidally split into two components (thereby providing three members within this family). In support of this idea, we find that no other asteroid with absolute magnitude H<=18.3 accompanies the known three members in the Lucascavin family. A similar result is found for the archetypal asteroid pair Rheinland-Kurpfalz.