From the Code of Canon Law;
Can. 435 A metropolitan, who is the archbishop of his diocese, presides offer an ecclesiastical province. The office of metropolitan is joined with an episcopal see determined or approved by the Roman Pontiff.
Can. 436 §1. In the suffragan dioceses, a metropolitan is competent:
1/ to exercise vigilance so that the faith and ecclesiastical discipline are observed carefully and to inform the Roman Pontiff of abuses, if there are any;
2/ to conduct a canonical visitation for a cause previously approved by the Apostolic See if a suffragan has neglected it;
3/ to designate a diocesan administrator according to the norm of cann. ⇒ 421, §2, and ⇒ 425, §3.
§2. Where circuмstances demand it, the Apostolic See can endow a metropolitan with special functions and power to be determined in particular law.
§3. The metropolitan has no other power of governance in the suffragan dioceses. He can perform sacred functions, however, as if he were a bishop in his own diocese in all churches, but he is first to inform the diocesan bishop if the church is the cathedral.
Can. 437 §1. Within three months from the reception of episcopal consecration or if he has already been consecrated, from the canonical provision, a metropolitan is obliged to request the pallium from the Roman Pontiff either personally or through a proxy. The pallium signifies the power which the metropolitan, in communion with the Roman Church, has by law in his own province.
§2. A metropolitan can use the pallium according to the norm of liturgical laws within any church of the ecclesiastical province offer which he presides, but not outside it, even if the diocesan bishop gives his assent.
§3. A metropolitan needs a new pallium if he is transferred to another metropolitan see.
http://www.vatican.va/archive/ENG1104/__P1J.HTM