  A large family of new black hole solutions in 2+1-dimensional
Einstein-Power-Maxwell (EPM) gravity with prescribed physical properties is
derived. We show with particular examples that according to the power parameter
k of the Maxwell field, the obtained solutions may be asymptotically flat for
1/2<k<1 or non-flat for k>1 in the vanishing cosmological constant limit. We
study the thermodynamic properties of the solution with two different models
and it is shown that thermodynamic quantities satisfy the first law. The
behaviour of the heat capacity indicates that by employing the 1+1-dimensional
dilaton analogy the local thermodynamic stability is satisfied.
