In this note, we prove that Kim-dividing over models is always witnessed by a coheir Morley sequence in NATP theories.Following the strategy of Chernikov and Kaplan [8], we obtain some corollaries which hold in NATP theories. Namely, (i) if a formula Kim-forks over a model, then it quasi-divides over the same model, (ii) for any tuple of parameters b and a model M , there exists a global coheirWe also show that in NATP theories, condition (ii) above is a necessary condition for being a witness coheir, assuming the existence of witnesses (see Definition 4.1 in this note). That is, if we assume that a witness coheir for Kim-dividing always exists over any given model, then a coheir p ⊇ tp(a/M ) must satisfy (ii) whenever it is a witness for Kim-dividing of a over a model M . We also give a sufficient condition for the existence of witness coheirs in terms of pre-independence relations.At the end of the paper, we leave a short remark on Mutchnik's recent work [16]. We point out that in ω-NDCTP 2 theories, a subclass of the class of NATP theories, Kim-forking and Kim-dividing are equivalent over models, where Kim-dividing is defined with respect to invariant Morley sequences, instead of coheir Morley sequences as in [16].

We prove several preservation theorems for NATP and furnish several examples of NATP.First, we prove preservation of NATP for the parametrization and sum of the theories of Fraïssé limits of Fraïssé classes satisfying strong amalgamation property.Second, we prove preservation of NATP for two kinds of dense/co-dense expansions, that is, the theories of lovely pairs and of H-structures for geometric theories and dense/co-dense expansion on vector spaces.Third, we prove preservation of NATP for the generic predicate expansion and the pair of an algebraically closed field and its distinguished subfield; for the latter, not only NATP, but also preservations of NTP 1 and NTP 2 are considered.Fourth, we present some proper examples of NATP using the results proved in this paper. Most of all, we show that the model companion of the theory of algebraically closed fields with circular orders (ACFO) is NATP.