Undercooled phase exists behind glass phase with superheated medium-range order between Tg and Tn+ > Tm. The ordered volume fraction stays equal to the percolation threshold F ≅ 0.15 of broken bonds up to Tn+. The difference ΔTg between Tg(bulk) of films with thickness (h > h0) and Tg(h) of ultrathin films of thickness (h < h0) is a linear function of (h-ho). Dense layer with minimum thickness hr is grafted against substrate by isothermal annealing, rinsed to reduce film thickness below hr/F, and finally dewetted at Tg. Similar thickness prepared and annealed near Tm and heated above Tm contains residual crystallized layer dewetting at Tn+. The prefrozen layer reproduces the glassy grafted layer in a crystallized state up to Tn+. Melting heat and melting temperature Tm are linear functions of h for h < h0. Prefrozen layers are due to melt-memories leading to new scenarios of crystallization.