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Let B be the open unit ball in C^2 and let a, b, c be three points in C^2which do not lie in a complex line, such that the complex line through a and bmeets B and such that <a|b> is different from 1 if one of the points a, b is inB and the other in the complement of B and such that at least one of thenumbers <a|c>, <b|c> is different from 1. We prove that if a continuousfunction f on the sphere bB extends holomorphically into B along each complexline which passes through one of the points a, b, c then f extendsholomorphically through B. This generalizes recent work of L.Baracco who provedsuch a result in the case when the points a, b, c are contained in B. The proofis different from the one of Baracco and uses the following one variable resultwhich we also prove in the paper and which in the real analytic case followsfrom the work of M.Agranovsky: Let D be the open unit disc in C. Given a in Dlet C(a) be the family of all circles in D obtained as the images of circlescentered at the origin under an automorphism of D that maps the origin to a.Given distinct points a, b in D and a positive integer n, a continuous functionf on the closed unit disc extends meromorphically from every circle T in eitherC(a) or C(b) through the disc bounded by T with the only pole at the center ofT of degree not exceeding n if and only if f is of the form f(z) =g_0(z)+g_1(z)\bar z +...+ g_n(z)\bar z^n where the functions g_0, g_1, ..., g_nare holomorphic on D.

Meromorphic extensions from small families of circles and holomorphic extensions from spheres