The outage performances of three transmit antenna selection (TAS) strategies in AF (amplify-and-forward) multiple-input multiple-output (MIMO) relaying over independent and identically distributed Nakagami-m fading channels are investigated. In particular, asymptotic lower bounds on the outage probabilities of the TAS strategies are derived and diversity orders are analysed. The presented expressions are general for the three TAS strategies with an arbitrary antenna configuration and a fading environment with arbitrary values of severity parameters m≥0.5.