  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-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 superconformal 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-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. 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.
