f45[{x_, y_}] := {x + 1, y^2 + 1};
NestWhileList[f45, {0.1, 0.1}, "here I dont know"]

NestWhileList[f45, {0.1, 0.1}, Norm[Last[f45]]] < 1]

condition[vector_] := Norm[vector] < 10

f45[{x_, y_}] := {x + 1, y^2 + 1};
NestWhileList[f45, {0.1, 0.1}, condition]

(*
==> {{0.1, 0.1}, {1.1, 1.01}, {2.1, 2.0201}, {3.1, 5.0808}, {4.1,
   26.8146}}
*)

f45[{x_, y_}] := {x + 1, y^2 + 1}
With[{max = 2}, NestWhileList[f45, {0.1, 0.1}, Norm[#] < max &]]

f46[x_, y_] := {x + 1, y^2 + 1}
With[{max = 2}, NestWhileList[f46[#[[1]], #[[2]]] &, {0.1, 0.1}, Norm[#] < max &]]