The OGLE Collection of Variable Stars. Type II Cepheids in the Magellanic System

We present a nearly complete collection of type II Cepheids in the Magellanic System. The sample consists of 338 objects: 285 and 53 variables in the Large and Small Magellanic Clouds, respectively. Based on the pulsation periods and light-curve morphology, we classified 118 of our type II Cepheids as BL Her, 120 as W Vir, 34 as peculiar W Vir, and 66 as RV Tau stars. For all objects, we publish time-series VI photometry obtained during the OGLE-IV survey, from 2010 to the end of 2017. We present the most interesting individual objects in our collection: 16 type II Cepheids showing additional eclipsing or ellipsoidal variability, two RV Tau variables more than 2.5 mag fainter than other stars of this type in the LMC, an RVb star that drastically decreased the amplitude of the long-period modulation, type II Cepheids exhibiting significant amplitude and period changes, and an RV Tau star which undergoes interchanges of deep and shallow minima. We show that peculiar W Vir stars have markedly different spatial distribution than other subclasses of type II Cepheids, which indicates different evolutionary histories of these objects.