  Following the ideas from a paper by the same author, we prove abstract
maximal restriction results for the Fourier transform. Our results deal mainly
with maximal operators of convolution-type and $r-$average maximal functions.
As a by-product of our techniques we obtain spherical maximal restriction
estimates, as well as restriction estimates for $2-$average maximal functions,
answering thus points left open by V. Kova\v{c} and M\"uller, Ricci and Wright.
