Summary: In 1932 W. Sierpiński [Publ. Math. Univ. Belgrade 1, 125–128 (1932; Zbl 0005.39102)] proved that every real-valued separately continuous function defined on the plane \(\mathbb{R}^2\) is determined uniquely on any everywhere dense subset of \(\mathbb{R}^2\). Namely, if two separately continuous functions coincide of an everywhere dense subset of \(\mathbb{R}^2\), then they are equal at each point of the plane. Z. Piotrowski and E. J. Wingler [Quest. Answers Gen. Topology 15, No. 1, 15–19 (1997; Zbl 0872.54009)] showed that the above-mentioned results can be transferred to maps with values in completely regular spaces. They proved that if every separately continuous function \(f:X\times Y\to \mathbb{R}\) is feebly continuous, then for every completely regular space \(Z\) every separately continuous map defined on \(X\times Y\) with values in \(Z\) is determined uniquely on everywhere dense subset of \(X\times Y\). M. Henriksen and R. G. Woods [Topology Appl. 97, No. 1–2, 175–205 (1999; Zbl 0974.54001)] proved that for an infinite cardinal \(\aleph\), an \(\aleph^+\)-Baire space \(X\) and a topological space \(Y\) with countable \(\pi\)-character every separately continuous function \(f:X\times Y\to \mathbb{R}\) is also determined uniquely on everywhere dense subset of \(X\times Y\). Later, V. V. Myhajlyuk [Mat. Stud. 14, No. 2, 193–196 (2000; Zbl 0979.54016)] proved the same result for a Baire space \(X\), a topological space \(Y\) with countable \(\pi\)-character and Urysohn space \(Z\). Moreover, it is natural to consider weaker conditions than separate continuity. The results in this direction were obtained by V. K. Maslyuchenko and O. I. Filipchuk [ibid. 47, No. 1, 91–99 (2017; Zbl 1414.54008)]. They proved that if \(X\) is a Baire space, \(Y\) is a topological space with countable \(\pi\)-character, \(Z\) is Urysohn space, \(A\subseteq X\times Y\) is everywhere dense set, \(f:X\times Y\to Z\) and \(g:X\times Y\to Z\) are weakly horizontally quasi-continuous, continuous with respect to the second variable, equi-feebly continuous with respect to the first one and such that \(f\vert _A=g\vert _A\), then \(f=g\). In this paper we generalize all of the results mentioned above. Moreover, we analyze classes of topological spaces which are favorable for Sierpińsi-type theorems.