I will present a family of random (compact) integral operators which encode the distributions of the critically spiked "hard edge" eigenvalues, i.e., the bottom of the spectrum of certain Wishart/Laguerre ensembles. A potential source of interest in these objects is that they posses degenerations which reproduce the known deformed Tracy-Widom laws (corresponding to the spiked "soft edge"). Many probabilistic/analytic questions remain, as I will describe. Joint work with Jose Ramirez (Univ. Costa Rica).