In all of these cases.
Elimination reaction compete with nucleophilic substitution reaction and is favored under conditions of
The heat help to reach the energy required for the dehydrohalogenation reaction with a strong base.
terc-butoxide favor the Hoffman elimination product, terc-butoxide tendency is to break out Zaitseff rule, so in this case the eliminitation in alkyl halides less substituted is favored.
If the substrate of the reaction is an 3rd alkyl halides, the carbocation is more stable so according to Zaitsev's rule in an elimination reaction, the most substituted product will be the most stable, so will be favored.
The nucleophile might to be a strong base because should be strong enough to form a bond with a hydrogen from the alkyl halide and let reaction continues. Regarding to 2° alkyl halide, 3° alkyl halide is favored towards 2° alkyl halide. Being the relative rate of reaction with 3° alkyl halide higher than 2° alkyl halide. That is because provides a greater number of hydrogens for attack by base and hence more favorable for elimination. If the alkyl halide are more branched more stable the alkene.
