Outline The TAGE predictor [12] is considered as one of the most storage effective global branch/path history predictors. It has been shown that associated with small adjunct predic-tors like a statistical corrector (SC for short) and/or a loop predictor (L for short) [11, 10], TAGE can even be more ef-fective. In this study, we explore the performance limits of these TAGE-SC-L predictors for respectively 32Kbits stor-age budget, 256 Kbits storage budget and quasi-unlimited (< 2 Gbits) storage budget. With a 32Kbits storage budget, only a very limited stor-age budget can be invested in the adjunct predictors. Then our submitted predictor used most of its storage budget on the TAGE predictor and features only a small loop predictor LP and a simple corrector filter CF. The submitted 32Kbits predictor achieves 3.315 MPKI on the CBP-4 traces. With a larger storage budget, one can invest more signifi-cant storage budget in the adjunct predictors. The submitted 256Kbits TAGE-SC-L predictor features a TAGE predictor, a loop predictor LP and a quite complex (≈ 45 Kbits) statis-tical corrector SC that exploits local history, global branch history and return-associated branch history. The 256Kbits TAGE-SC-L predictor achieves 2.365 MPKI on the CBP-4 traces. The no-limit budget allows to use a statistical corrector build with many components exploiting global branch and path histories, local histories and some form of skeleton his-tories. The submitted predictor achieves 1.782 MPKI on the CBP-4 traces.