The prediction tables of stellar occultations by 5 Centaurs and 34 TNOs (referred simply as TNOs hereafter) for the period 2012.5-2014 were built to support the investigation of the physical properties of (8405) Asbolus, (24835) 1995 SM55, (10199) Chariklo, (26375) 1999 DE9, (47171) 1999 TC36, (38628) Huya, (54598) Bienor, (55565) 2002 AW197, (55576) Amycus, (83982) Crantor, (119951) 2002 KX14, (307261) 2002 MS4, (84522) 2002 TC302, (55637) 2002 UX25, (55638) 2002 VE95, (119979) 2002 WC19, (120132) 2003 FY128, (174567) 2003 MW12, (120178) 2003 OP32, 2003 UZ413, (84922) 2003 VS2, (90568) 2004 GV9, 2004 NT33, (175113) 2004 PF115, (120347) Salacia, (120348) 2004 TY364, (144897) 2004 UX10, 2005 CC79 (2011 FX62), (303775) 2005 QU182, (145451) 2005 RM43, (145452) 2005 RN43, (145453) 2005 RR43, (202421) 2005 UQ513, 2007 JH43, (278361) 2007 JJ43, (225088) 2007 OR10, (229762) 2007 UK126, 2008 OG19, and 2010 EK139 for this period. These objects are important to understand the structure, origin, and evolution of the outer solar system. Our goal was to derive precise predictions. With this aim, we constructed astrometric star catalogues in the UCAC4 system covering their sky paths. For that, we carried out during 2011-2013 an observational program at the ESO2p2/WFI instrument covering the sky path of these 39 TNOs for the period 2012.5-2014. We made the astrometry of 550 GB of images with the Platform for Reduction of Astronomical Images Automatically (PRAIA). By relatively simple astrometric techniques, we treated the overlapping observations and derived a field distortion pattern for the WFI mosaic of CCDs to within 50mas precision. The catalogue star positions were obtained in the UCAC4 frame with uncertainties of 40mas for stars up to magnitude completeness (about R=19). New stellar proper motions were also determined with 2MASS and the USNO B1.0 catalogue positions as first epoch. The catalogues for all TNOs contain in all more than 12.4 million entries, covering the sky paths of the objects with 30 arcmin width. The magnitude completeness is about R=19 with a limit about R=21. Ephemeris offsets with about 10mas to 100mas precision were applied for each TNO orbit to improve the predictions. They were obtained during 2011-2013 from a parallel observational campaign carried out with telescope diameters from 0.6m to 2.2m. The 7343 candidate stars listed in the prediction tables were searched using a proximity radius of 650mas with the geocentric apparent orbit (corrected by ephemeris offsets) of the body considered. This radius is a little more than seven times the apparent radius of a body with Pluto's size (50mas) plus the apparent Earth radius (285 mas) as projected in the sky plane at 31AU (about the Pluto-Earth distance for 2008-2015). No threshold in R magnitude was used in the search for candidates, as relatively faint R objects may turn out to be bright infrared stars, perfect targets for the SOFIA observatory and for ground-based instruments well equipped with J, H, or K band detectors (J, H, and K magnitudes are promptly available in the tables if the star belongs to the 2MASS). Besides, events may be also favoured by slow shadow speeds of less than 20km/s. Also, no constraint on a geographic place was applied, as in principle SOFIA observations can be done from any sub-solar point on Earth. Events in daylight at sub-planet point were not excluded either, as they could yet be observable in the dark, right above the horizon, from places near the Earth terminator. We furnish here prediction tables for future and also for past stellar occultations covering the sky paths between 2012.5-2014. The importance of predictions for occultations still to come is obvious. But the predictions of past occultations are also useful for at least three reasons. First, they can be used by anyone as reference for ongoing fittings of light curves of recent past observed events. Second, they serve to derive ephemeris drifts by comparing expected and observed central instants and C/A values. Finally, they can be used as an external check for the accuracy and precision of our prediction tables. In all, for R=19 stars (catalogue magnitude completeness) and 40mas errors in the WFI positions, we may assume a bulk error of about 80mas for C/A, dominated by the ephemeris offsets errors of about 70mas. For about 40AU, this implies a shadow path uncertainty over the Earth of the order of 2300km. If the ephemeris offsets can be well determined to within 30mas precision, then a bulk error of 50mas in C/A can be achieved, leading to a precision of about 1400km for the WFI occultation path predictions. Thus, the probability of actually observing the occultation is not as high as hoped, but not despairingly small, especially if the event occurs above a dense, populated region in terms of astronomers, including amateurs, with access to telescopes.
