T-polynomial convexity and holomorphic convexity

We compare the T-polynomial convexity of Guedj with holomorphic convexity away from the support of T. In particular we show an Oka--Weil theorem for T-polynomial convexity, as well as present a situation when the notions of T-polynomial convexity and holomorphic convexity of X T coincide in the context of complex projective algebraic manifolds.