Solutions of the Riccati equationW′ +W2=e2zare known to be asymptotic toezore-z. We show that those solutions which are asymptotic toezhaveregular growthoverC(ez) as z→∞ in funnel-like regionsDbetween curves of the form. Here the notion of regular growth over a differential fieldHof holomorphic germs onDis inspired by real Hardy field theory and is a generalization of the classical notion of non-oscillation. It means that for any differential polynomialP(X,X′,…) with coefficients inH, the functionP(W,W′,…) is ultimately zero free inDor identically zero.