We propose general relations between the conformal anomaly and the chiral (R-symmetry and gravitational) anomaly coefficients in 6d (1, 0) superconformal theories. The suggested expressions for the three type B conformal anomaly c i -coefficients complement the expression for the type A anomaly a-coefficient found in arXiv:1506.03807 . We check them on several examples — the standard (1, 0) hyper and tensor multiplets as well as some higher derivative short multiplets containing vector fields that generalize the super-conformal 6d vector multiplet discussed in arXiv:1506.08727 . We also consider a family of higher derivative superconformal (2, 0) 6d multiplets associated to 7d multiplets in the KK spectrum of 11d supergravity compactified on S 4 . In particular, we prove that (2,0) 6d conformal supergravity coupled to 26 tensor multiplets is free of all chiral and conformal anomalies. We discuss some interacting (1, 0) superconformal theories, predicting the c i -coefficients for the “E-string” theory on multiple M5-branes at E 8 9-brane and for the theory describing M5-branes at an orbifold singularity ℂ 2 / Γ $$ {\mathrm{\mathbb{C}}}^2/\Gamma $$ . Finally, we elaborate on holographic computation of subleading corrections to conformal anomaly coefficients coming from R 2 + R 3 terms in 7d effective action, revisiting, in particular, the (2,0) theory case.