I don't know the actual numbers, but in the New York market, United is the smallest of the big three carriers in scale and scope of operations, but it does have a very sizeable chunk of the transcon market and flights to major international destinations:
Nonstop to LHR (pre 9/11, three daily, including one 777), NRT, GRU, EZE, SEA, LAX, SFO, BOS, and SJU (week-end only).
Aircraft: B777, B767-200, B767-300ER, A320, B737-500 (for the Boston route), and the B757 to SJU.
Nonstop to LAX, SFO, DEN, ORD, MIA, IAD and London/Heathrow.
Aircraft: B777, B767-200, B757, A320, A319, B737-300/500, turboprops for some United Express markets.
Nonstop to ORD (hourly), DEN, IAD (hourly), and MIA.
CRJ, A320, A319, B757, B737-300/500
Nonstop to IAD and ORD