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It is proved that every remainder of a nonlocally compact semitopological group 
$G$ is a Baire space if and only if 
$G$ is not Čech-complete, which improves a dichotomy theorem of topological groups by Arhangel’skiǐ [‘The Baire property in remainders of topological groups and other results’, Comment. Math. Univ. Carolin. 50(2) (2009), 273–279], and also gives a positive answer to a question of Lin and Lin [‘About remainders in compactifications of paratopological groups’, ArXiv: 1106.3836v1 [Math. GN] 20 June 2011]. We also show that for a nonlocally compact rectifiable space 
$G$ every remainder of 
$G$ is either Baire, or meagre and Lindelöf.
