  Although the title seems self-contradictory, it does not contain a misprint.
The model we study is a seemingly minor modification of the "true self-avoiding
walk" (TSAW) model of Amit, Parisi, and Peliti in two dimensions. The walks in
it are self-repelling up to a characteristic time $T^*$ (which depends on
various parameters), but spontaneously (i.e., without changing any control
parameter) become self-trapping after that. For free walks, $T^*$ is
astronomically large, but on finite lattices the transition is easily
observable. In the self-trapped regime, walks are subdiffusive and
intermittent, spending longer and longer times in small areas until they escape
and move rapidly to a new area. In spite of this, these walks are extremely
efficient in covering finite lattices, as measured by average cover times.
