A¹-homotopy type of $A^2 \{(0,0) \}$

In this article we prove that any A¹-connected smooth k-variety is A¹-uniruled for any algebraically closed field k. We establish that if a non empty open subscheme X of a smooth affine k-scheme is A¹-weakly equivalent to A²ₖ \(0,0) \, then X A²ₖ \(0,0) \ as k-varieties for any field k of characteristic $0$.