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We proved a truncated second main theorem of level one with explicitexceptional sets for analytic maps into $\mathbb P^2$ intersecting thecoordinate lines with sufficiently high multiplicities. As applications, westudied some cases of Campana's orbifold conjecture for $\mathbb P^2$ andfinite ramified covers of $\mathbb P^2$ with three components admittingsufficiently large multiplicities.

A complex case of Vojta's general abc conjecture and cases of Campana's orbifold conjecture