Relation between impulse response and Region of convergence?
For a discrete-time system if the impulse response is IIR and right sided, then the ROC will be outside of the largest pole. Else if the impulse response is IIR and left sided, then the ROC will be inside of the smallest pole. 

For all FIR (finite inpulse response) systems, the ROC will be all $z$ except possibly zero and/or infinity.

For the continuous-time systems, for right sided impulse responses, the ROC will be to the right (half plane) of the max pole, and for left sided impulse responses it will be to the left of the minimum pole.